The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, w...The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.展开更多
Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a...Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.展开更多
Many physical systems can be successfully modelled using equations that admit the soliton solutions.In addition,equations with soliton solutions have a significant mathematical structure.In this paper,we study and ana...Many physical systems can be successfully modelled using equations that admit the soliton solutions.In addition,equations with soliton solutions have a significant mathematical structure.In this paper,we study and analyze a three-dimensional soliton equation,which has applications in plasma physics and other nonlinear sciences such as fluid mechanics,atomic physics,biophysics,nonlinear optics,classical and quantum fields theories.Indeed,solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour.We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time.Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function,elliptic functions,elementary trigonometric and hyperbolic functions solutions of the equation.Besides,various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique.These solutions comprise dark soliton,doubly-periodic soliton,trigonometric soliton,explosive/blowup and singular solitons.We further exhibit the dynamics of the solutions with pictorial representations and discuss them.In conclusion,we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula.We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.展开更多
Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundar...Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.展开更多
This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the pr...The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the propagation characteristics of gravity waves(GWs) over Northwest China. We found that obvious seasonal variations occur in the propagation of GWs. In spring, GWs mainlypropagate in the northeast direction. In summer and autumn, GWs mainly propagate in the north direction. However, GWs mainlypropagate in the south direction in winter. The direction of GW propagation in the zonal direction is controlled by the wind-filteringeffect, whereas the north–south meridional direction is mainly determined by the location of the wave source. We found that the averageenergy spectrum exhibits a 10%–20% higher intensity in summer and winter compared with spring and autumn. For the first time, wereport the seasonal variation characteristics of GWs over the inland areas of Northwest China, which is of great significance forunderstanding the regional distribution characteristics of GWs.展开更多
This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Ya...This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).展开更多
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach...The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.展开更多
Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl e...Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl exible FD stencil,which requires pairing and centrosymmetricity of the involved gridpoints,is used on the basis of the 2D L-F domain acoustic wave equation.The L-F domain numerical dispersion analysis is then performed by minimizing the phase error of the normalized numerical phase and attenuation propagation velocities to obtain the optimization coefficients.An optimal FD forward modeling method is finally developed for the L-F domain acoustic wave equation and applied to the traditional standard 9-point scheme and 7-and 9-point schemes,where the latter two schemes are used in discontinuous-grid FD modeling.Numerical experiments show that the optimal L-F domain FD modeling method not only has high accuracy but can also be applied to equal and unequal directional sampling intervals and discontinuous-grid FD modeling to reduce computational cost.展开更多
We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We s...We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.展开更多
The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a c...The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.展开更多
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-eliminati...Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-elimination(IME)methods,how to increase accuracy and reduce cost of IME still poses a significant challenge.A new method is proposed to effectively and efficiently eliminate internal multi-ples,along with its application in internal-multiple-eliminated-migration(IMEM),addressing this issue.This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation,which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously,and complete internal-multiple-elimination processing,adaptively and effi-ciently.The proposed method has several features:(1)input data is same as that for conventional migration:source signature(used for migration only),macro velocity model,and receiver data,without additional requirements for source/receiver sampling;(2)method is efficient,without need of iterative calculations(which are typically needed for most of IME algorithms);and(3)method is cost effective:IME is completed in the same depth-extrapolation scheme of IMEM,without need of a separate pro-cessing and additional cost.Several synthesized data models are used to test the proposed method:one-dimensional model,horizontal layered model,multi-layer model with one curved layer,and SEG/EAGE Salt model.Additionally,we perform a sensitivity analysis of velocity using smoothed models.This analysis reveals that although the accuracy of velocity measurements impacts our proposed method,it significantly reduces internal multiple false imaging compared to traditional RTM techniques.When applied to actual seismic data from a carbonate reservoir zone,our method demonstrates superior clarity in imaging results,even in the presence of high-velocity carbonate formations,outperforming conven-tional migration methods in deep strata.展开更多
In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the...In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.展开更多
A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak...A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak value of the 1-breather solution are calculated.Additionally,through the asymptotic analysis of 2-breather solution,we show that two breathers undergo an elastic collision.By applying the generalized long-wave limit method,the fundamental and second-order rogue wave solutions for the complex m Kd V equation are obtained from the 1-breather and 2-breather solutions,respectively.We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex m Kd V equation from the 2-breather solution.Furthermore,the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex m Kd V equation are derived from the 3-breather solution via the generalized long-wave limit method.By controlling the phase parameters of breathers,the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.展开更多
A three-dimensional（3D） parabolic equation（PE） model for sound propagation in a seismo-acoustic waveguide is developed in Cartesian coordinates, with x, y, and z representing the marching direction, the longitudin...A three-dimensional（3D） parabolic equation（PE） model for sound propagation in a seismo-acoustic waveguide is developed in Cartesian coordinates, with x, y, and z representing the marching direction, the longitudinal direction, and the depth direction, respectively. Two sets of 3D PEs for horizontally homogenous media are derived by rewriting the 3D elastic motion equations and simultaneously choosing proper dependent variables. The numerical scheme is for now restricted to the y-independent bathymetry. Accuracy of the numerical scheme is validated, and its azimuthal limitation is analyzed. In addition, effects of horizontal refraction in a wedge-shaped waveguide and another waveguide with a polyline bottom are illustrated. Great efforts should be made in future to provide this model with the ability to handle arbitrarily irregular fluid-elastic interfaces.展开更多
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite differenc...This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.展开更多
基金supported by the National Natural Science Foundation of China (11171208)Shanghai Leading Academic Discipline Project (S30106)
文摘The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.
基金supported by the National Natural Science Foundation of China(No.41474110)Shell Ph.D. Scholarship to support excellence in geophysical research
文摘Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.
文摘Many physical systems can be successfully modelled using equations that admit the soliton solutions.In addition,equations with soliton solutions have a significant mathematical structure.In this paper,we study and analyze a three-dimensional soliton equation,which has applications in plasma physics and other nonlinear sciences such as fluid mechanics,atomic physics,biophysics,nonlinear optics,classical and quantum fields theories.Indeed,solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour.We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time.Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function,elliptic functions,elementary trigonometric and hyperbolic functions solutions of the equation.Besides,various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique.These solutions comprise dark soliton,doubly-periodic soliton,trigonometric soliton,explosive/blowup and singular solitons.We further exhibit the dynamics of the solutions with pictorial representations and discuss them.In conclusion,we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula.We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.
文摘Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by the National Science Foundation of China(Grant Nos.42374205 and 41974179)the Specialized Research Fund of the National Space Science Center,Chinese Academy of Sciences(Grant No.E4PD3010)supported by the Specialized Research Fund for State Key Laboratories.
文摘The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the propagation characteristics of gravity waves(GWs) over Northwest China. We found that obvious seasonal variations occur in the propagation of GWs. In spring, GWs mainlypropagate in the northeast direction. In summer and autumn, GWs mainly propagate in the north direction. However, GWs mainlypropagate in the south direction in winter. The direction of GW propagation in the zonal direction is controlled by the wind-filteringeffect, whereas the north–south meridional direction is mainly determined by the location of the wave source. We found that the averageenergy spectrum exhibits a 10%–20% higher intensity in summer and winter compared with spring and autumn. For the first time, wereport the seasonal variation characteristics of GWs over the inland areas of Northwest China, which is of great significance forunderstanding the regional distribution characteristics of GWs.
基金Supported by the National Natural Science Foundation of China (12071162)the Natural Science Foundation of Fujian Province (2025J01168)。
文摘This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The Boussinesq equations,pivotal in the analysis of water wave dynamics,effectively model weakly nonlinear and long wave approximations.This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation.The solutions are articulated through soliton,trigonometric,rational,and Jacobi elliptic functions.Notably,the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement.Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed.The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics,thereby enhancing comprehension of the physical attributes and dynamics of water waves.
基金National Natural Science Foundation of China(no.41604037)Natural Science Foundation of Hubei Province(no.2022CFB125)+2 种基金Open Fund of Key Laboratory of Exploration Technologies for Oil and Gas Resources(Yangtze University)Ministry of Education(no.K2021-09)College Students'Innovation and Entrepreneurship Training Program(no.2019053)。
文摘Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl exible FD stencil,which requires pairing and centrosymmetricity of the involved gridpoints,is used on the basis of the 2D L-F domain acoustic wave equation.The L-F domain numerical dispersion analysis is then performed by minimizing the phase error of the normalized numerical phase and attenuation propagation velocities to obtain the optimization coefficients.An optimal FD forward modeling method is finally developed for the L-F domain acoustic wave equation and applied to the traditional standard 9-point scheme and 7-and 9-point schemes,where the latter two schemes are used in discontinuous-grid FD modeling.Numerical experiments show that the optimal L-F domain FD modeling method not only has high accuracy but can also be applied to equal and unequal directional sampling intervals and discontinuous-grid FD modeling to reduce computational cost.
基金partially supported by the National Natural Science Foundation of China(Grant No.12201417)the Project funded by the China Postdoctoral Science Foundation(Grant No.2023M733173)partially supported by the National Natural Science Foundation of China(Grant No.12375006)。
文摘We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.
基金supported by the National Natural Science Foundation of China(Grant No.12071432)Zhejiang Provincial Natural Science Foundation(Grant No.LZ24A010007)。
文摘The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.
基金Supported by National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
基金supported by the National Natural Science Foundation of China(Grant No.42004103)Sichuan Science and Technology Program(2023NSFSC0257)the CNPC Innovation Found(2022DQ02-0306).
文摘Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-elimination(IME)methods,how to increase accuracy and reduce cost of IME still poses a significant challenge.A new method is proposed to effectively and efficiently eliminate internal multi-ples,along with its application in internal-multiple-eliminated-migration(IMEM),addressing this issue.This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation,which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously,and complete internal-multiple-elimination processing,adaptively and effi-ciently.The proposed method has several features:(1)input data is same as that for conventional migration:source signature(used for migration only),macro velocity model,and receiver data,without additional requirements for source/receiver sampling;(2)method is efficient,without need of iterative calculations(which are typically needed for most of IME algorithms);and(3)method is cost effective:IME is completed in the same depth-extrapolation scheme of IMEM,without need of a separate pro-cessing and additional cost.Several synthesized data models are used to test the proposed method:one-dimensional model,horizontal layered model,multi-layer model with one curved layer,and SEG/EAGE Salt model.Additionally,we perform a sensitivity analysis of velocity using smoothed models.This analysis reveals that although the accuracy of velocity measurements impacts our proposed method,it significantly reduces internal multiple false imaging compared to traditional RTM techniques.When applied to actual seismic data from a carbonate reservoir zone,our method demonstrates superior clarity in imaging results,even in the presence of high-velocity carbonate formations,outperforming conven-tional migration methods in deep strata.
基金supported by the National Natural Science Foundation of China(12371255,11975306)the Xuzhou Basic Research Program Project(KC23048)+1 种基金the Six Talent Peaks Project in Jiangsu Province(JY-059)the 333 Project in Jiangsu Province and the Fundamental Research Funds for the Central Universities of CUMT(2024ZDPYJQ1003).
文摘In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12061051 and 12461048)。
文摘A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak value of the 1-breather solution are calculated.Additionally,through the asymptotic analysis of 2-breather solution,we show that two breathers undergo an elastic collision.By applying the generalized long-wave limit method,the fundamental and second-order rogue wave solutions for the complex m Kd V equation are obtained from the 1-breather and 2-breather solutions,respectively.We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex m Kd V equation from the 2-breather solution.Furthermore,the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex m Kd V equation are derived from the 3-breather solution via the generalized long-wave limit method.By controlling the phase parameters of breathers,the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.
基金Project supported by the National Nature Science Foundation of China(Grant Nos.11234002 and 11704337)the National Key Research Program of China(Grant No.2016YFC1400100)
文摘A three-dimensional（3D） parabolic equation（PE） model for sound propagation in a seismo-acoustic waveguide is developed in Cartesian coordinates, with x, y, and z representing the marching direction, the longitudinal direction, and the depth direction, respectively. Two sets of 3D PEs for horizontally homogenous media are derived by rewriting the 3D elastic motion equations and simultaneously choosing proper dependent variables. The numerical scheme is for now restricted to the y-independent bathymetry. Accuracy of the numerical scheme is validated, and its azimuthal limitation is analyzed. In addition, effects of horizontal refraction in a wedge-shaped waveguide and another waveguide with a polyline bottom are illustrated. Great efforts should be made in future to provide this model with the ability to handle arbitrarily irregular fluid-elastic interfaces.
文摘This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
