This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
Tin(Sn)-lead(Pb)mixed halide perovskites have attracted widespread interest due to their wider re-sponse wavelength and lower toxicity than lead halide perovskites,Among the preparation methods,the two-step method mor...Tin(Sn)-lead(Pb)mixed halide perovskites have attracted widespread interest due to their wider re-sponse wavelength and lower toxicity than lead halide perovskites,Among the preparation methods,the two-step method more easily controls the crystallization rate and is suitable for preparing large-area per-ovskite devices.However,the residual low-conductivity iodide layer in the two-step method can affect carrier transport and device stability,and the different crystallization rates of Sn-and Pb-based per-ovskites may result in poor film quality.Therefore,Sn-Pb mixed perovskites are mainly prepared by a one-step method.Herein,a MAPb_(0.5)Sn_(0.5)I_(3)-based self-powered photodetector without a hole transport layer is fabricated by a two-step method.By adjusting the concentration of the ascorbic acid(AA)addi-tive,the final perovskite film exhibited a pure phase without residues,and the optimal device exhibited a high responsivity(0.276 A W^(-1)),large specific detectivity(2.38×10^(12) Jones),and enhanced stability.This enhancement is mainly attributed to the inhibition of Sn2+oxidation,the control of crystal growth,and the sufficient reaction between organic ammonium salts and bottom halides due to the AA-induced pore structure.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Und...In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.展开更多
Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently so...Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series meth...By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.展开更多
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.展开更多
In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p...In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.展开更多
In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary condi...In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary conditions having parameter in two cases f(O)=0 and f(0)>0 by using upper and lower solution method,where λ>0 is a parameter,f∈C^(2)([0,∞),R)is monotonically increasing and lim_(μ→1)^(f(u)/1-u=0,h∈C^(1)([0,1],(0,∞))is a nonincreasing function and h(t)>1.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b...This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.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
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
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep...In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.展开更多
In this study,we investigate a variety of exact soliton solutions of general(2+1)-dimensional Bogoyavlensky–Konopelchenko equation via the exp(-Φ(η))-expansion method and modified Kudryashov method.The exact soluti...In this study,we investigate a variety of exact soliton solutions of general(2+1)-dimensional Bogoyavlensky–Konopelchenko equation via the exp(-Φ(η))-expansion method and modified Kudryashov method.The exact solutions are characterized in the form of hyperbolic,trigonometric and rational function solutions using exp(-Φ(η))-expansion method,whereas the solution in the form of hyperbolic function expression is obtained by the modified Kudryashov method.These exact solutions also include kink,bright,dark,singular and periodic soliton solutions.The graphical interpretation of the exact solutions is addressed for specific choices of the parameters appearing in the solutions.展开更多
The double-beam system is a crucial foundational structure in industry,with extensive application contexts and significant research value.The double-beam system with damping and gyroscopic effects is termed as the dam...The double-beam system is a crucial foundational structure in industry,with extensive application contexts and significant research value.The double-beam system with damping and gyroscopic effects is termed as the damped gyroscopic double-beam system.In such systems,the orthogonality conditions of the undamped double-beam system are no longer applicable,rendering it impossible to decouple them in modal space using the modal superposition method(MSM) to obtain analytical solutions.Based on the complex modal method and state space method,this paper takes the damped pipe-in-pipe(PIP) system as an example to solve this problem.The concepts of the original system and adjoint system are introduced,and the orthogonality conditions of the damped PIP system are given in the state-space.Based on the derived orthogonality conditions,the transient and steady-state response solutions are obtained.In the numerical discussion section,the convergence and accuracy of the solutions are verified.In addition,the dynamic responses of the system under different excitations and initial conditions are studied,and the forward and reverse synchronous vibrations in the PIP system are discussed.Overall,the method presented in this paper provides a convenient way to analyze the dynamics of the damped gyroscopic double-beam system.展开更多
In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting device...In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.展开更多
We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular ma...We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Natural Science Foun-dation of China(Nos.52025028,52332008,52372214,52202273,and U22A20137)the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions.
文摘Tin(Sn)-lead(Pb)mixed halide perovskites have attracted widespread interest due to their wider re-sponse wavelength and lower toxicity than lead halide perovskites,Among the preparation methods,the two-step method more easily controls the crystallization rate and is suitable for preparing large-area per-ovskite devices.However,the residual low-conductivity iodide layer in the two-step method can affect carrier transport and device stability,and the different crystallization rates of Sn-and Pb-based per-ovskites may result in poor film quality.Therefore,Sn-Pb mixed perovskites are mainly prepared by a one-step method.Herein,a MAPb_(0.5)Sn_(0.5)I_(3)-based self-powered photodetector without a hole transport layer is fabricated by a two-step method.By adjusting the concentration of the ascorbic acid(AA)addi-tive,the final perovskite film exhibited a pure phase without residues,and the optimal device exhibited a high responsivity(0.276 A W^(-1)),large specific detectivity(2.38×10^(12) Jones),and enhanced stability.This enhancement is mainly attributed to the inhibition of Sn2+oxidation,the control of crystal growth,and the sufficient reaction between organic ammonium salts and bottom halides due to the AA-induced pore structure.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by NSFC(No.12561023)partly by the Provincial Natural Science Foundation of Jiangxi,China(Nos.20232BAB201001,20202BAB211004)。
文摘In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.
基金Supported by NSFC (No.12371378)NSF of Fujian Province (Nos.2024J01980,2023J01955)。
文摘Analysis and design of linear periodic control systems are closely related to the periodic matrix equations.The biconjugate residual method(BCR for short)have been introduced by Vespucci and Broyden for efficiently solving linear systems Aα=b.The objective of this paper is to provide one new iterative algorithm based on BCR method to find the symmetric periodic solutions of linear periodic matrix equations.This kind of periodic matrix equations has not been dealt with yet.This iterative method is guaranteed to converge in a finite number of steps in the absence of round-off errors.Some numerical results are performed to illustrate the efficiency and feasibility of new method.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
文摘By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.
基金supported by the NSFC(11301297)the Hubei Provincial Natural Science Foundation of China(2024AFB730)+3 种基金the Yichang City Natural Science Foundation(A-24-3-008)the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003)Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014)the NFSC(12101577).
文摘In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.
文摘In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.
基金Supported by the National Natural Science Foundation of China(12361040)。
文摘In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary conditions having parameter in two cases f(O)=0 and f(0)>0 by using upper and lower solution method,where λ>0 is a parameter,f∈C^(2)([0,∞),R)is monotonically increasing and lim_(μ→1)^(f(u)/1-u=0,h∈C^(1)([0,1],(0,∞))is a nonincreasing function and h(t)>1.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金Supported by Research Start-up Fund of Jianghan University(06050001).
文摘This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
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Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。
文摘In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.
文摘In this study,we investigate a variety of exact soliton solutions of general(2+1)-dimensional Bogoyavlensky–Konopelchenko equation via the exp(-Φ(η))-expansion method and modified Kudryashov method.The exact solutions are characterized in the form of hyperbolic,trigonometric and rational function solutions using exp(-Φ(η))-expansion method,whereas the solution in the form of hyperbolic function expression is obtained by the modified Kudryashov method.These exact solutions also include kink,bright,dark,singular and periodic soliton solutions.The graphical interpretation of the exact solutions is addressed for specific choices of the parameters appearing in the solutions.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘The double-beam system is a crucial foundational structure in industry,with extensive application contexts and significant research value.The double-beam system with damping and gyroscopic effects is termed as the damped gyroscopic double-beam system.In such systems,the orthogonality conditions of the undamped double-beam system are no longer applicable,rendering it impossible to decouple them in modal space using the modal superposition method(MSM) to obtain analytical solutions.Based on the complex modal method and state space method,this paper takes the damped pipe-in-pipe(PIP) system as an example to solve this problem.The concepts of the original system and adjoint system are introduced,and the orthogonality conditions of the damped PIP system are given in the state-space.Based on the derived orthogonality conditions,the transient and steady-state response solutions are obtained.In the numerical discussion section,the convergence and accuracy of the solutions are verified.In addition,the dynamic responses of the system under different excitations and initial conditions are studied,and the forward and reverse synchronous vibrations in the PIP system are discussed.Overall,the method presented in this paper provides a convenient way to analyze the dynamics of the damped gyroscopic double-beam system.
基金Project supported by the Science and Technology Plan Joint Program of Liaoning Province of China(Natural Science Foundation-Doctoral Research Launch Project)(No.2024-BSLH-027)the Fundamental Research Funds for Undergraduate Universities of Liaoning Province of China(No.LJBKY2024033)+1 种基金the National Natural Science Foundation of China(No.12472064)the Natural Science Foundation of Liaoning Province of China(No.2023-MS-118)。
文摘In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.
基金supported by the National Natural Science Foundation of China(1237119112071175)+4 种基金supported by the NSFC(1207117511901080)supported by the NSFC(12071175)the Fundamental Research Funds For the Central Universities(2412023YQ003)the Natural Science Foundation of Jilin Province(20200201253JC)。
文摘We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.
