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
By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schroetinger equation derived from one important model in the study of atmospheric and ...By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schroetinger equation derived from one important model in the study of atmospheric and ocean dynamical systems. Our analytical solutions include bright and dark solitary waves, and periodical solutions, which can be used to explain atmospheric phenomena.展开更多
Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junction...Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices.Based on the Lax pair,the binary Darboux transformation is constructed under certain constraints,thus the multi-dark soliton solutions are presented.Soliton propagation and collision are graphically discussed with the group-velocity dispersion,third-and fourth-order dispersions,which can affect the solitons’velocities but have no effect on the shapes.Elastic collisions between the two dark solitons and among the three dark solitons are displayed,while the elasticity cannot be influenced by the above three coefficients.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutio...In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutions of（2＋1）-dimensional coupled higher-order nonlinear Schrodinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.展开更多
A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearit...A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.展开更多
In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowled...In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.展开更多
In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)...In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.展开更多
We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical ...We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.展开更多
The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By...The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
By using a simple transformation approach,we solve the higher-order nonlinear Schrödinger equation under another condition.The obtained exact soliton solutions have the following prominent features:The bright sol...By using a simple transformation approach,we solve the higher-order nonlinear Schrödinger equation under another condition.The obtained exact soliton solutions have the following prominent features:The bright soliton can propagate in both the normal and anormal regions;the soliton travelling speed is proportional to its amplitude square;the phase of the soliton is independent of its amplitude or width;and the component solitons of the bound soliton have the same phase.展开更多
In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing...In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing transformation with an asymptotic expansion method,the existence and properties of the one-,second-,and third-order RWs for the higher-order nonlinear Schrodinger equation are constructed.In addition,the main characteristics of these solutions are discussed through some graphics,which are draw widespread attention in a variety of complex systems such as optics,Bose-Einstein condensates,capillary fow,superfluidity,fluid dynamics,and finance.In addition,infinitely-many conservation laws are established.展开更多
The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the probl...The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.展开更多
We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new ...We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.展开更多
By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients,...By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.展开更多
A newly proposed method,i.e.the adaptive higher-order nonlinear finite impulse response(HONFIR)filter based on higher-order sparse Volterra series expansions,is introduced to predict hyper-chaotic time series.The effe...A newly proposed method,i.e.the adaptive higher-order nonlinear finite impulse response(HONFIR)filter based on higher-order sparse Volterra series expansions,is introduced to predict hyper-chaotic time series.The effectiveness of using adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including Mackey-Glass equation and 4-dimensional nonlinear dynamical system.A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series.Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.展开更多
When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order non...When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.展开更多
In this work,we develop an extended dissipaton theory that generalizes the environmental couplings beyond the conventional linear and quadratic forms,enabling the treatment of ar-bitrary order of bath couplings.Ap-ply...In this work,we develop an extended dissipaton theory that generalizes the environmental couplings beyond the conventional linear and quadratic forms,enabling the treatment of ar-bitrary order of bath couplings.Ap-plying this theoretical framework to the condensed-phase non-Condon spectroscopy,we demonstrate the in-terplay of anharmonicity,non-Con-don and solvent effects on optical spectra,where the higher-order cou-plings arise from the anharmonicity of nuclear potential surface of the excited state.Precise simulations are carried out with high efficiency on linear absorption spectra involving the above mentioned correlated effects.We exhibit how an anharmonic potential modulates the vibronic feature,offering insights into the role of nonlinear environmental couplings in spectroscopic signatures and exemplifying the success of the extended dissipaton formalism as an exact and efficient method for higher-or-der bath couplings.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
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The project supported by National Natural Science Foundations of China under Grant Nos. 90203001, 10475055, 40305009, and 10547124
文摘By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schroetinger equation derived from one important model in the study of atmospheric and ocean dynamical systems. Our analytical solutions include bright and dark solitary waves, and periodical solutions, which can be used to explain atmospheric phenomena.
基金supported by the National Natural Science Foundation of China under grant no.11905061by the Fundamental Research Funds for the Central Universities(No.9161718004)。
文摘Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices.Based on the Lax pair,the binary Darboux transformation is constructed under certain constraints,thus the multi-dark soliton solutions are presented.Soliton propagation and collision are graphically discussed with the group-velocity dispersion,third-and fourth-order dispersions,which can affect the solitons’velocities but have no effect on the shapes.Elastic collisions between the two dark solitons and among the three dark solitons are displayed,while the elasticity cannot be influenced by the above three coefficients.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
基金Supported by the National Natural Science Foundation of China under Grant No.61671227the Natural Science Foundation of Shandong Province under Grant No.ZR2014AM018
文摘In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutions of（2＋1）-dimensional coupled higher-order nonlinear Schrodinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.
基金the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024National Natural Science Foundation of China under Grant No.60372095
文摘A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.
文摘In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.
基金Supported by the National Natural Science Foundation of China under Grant No.61671227the Natural Science Foundation of Shandong Province in China under Grant No.ZR2014AM018
文摘In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schr¨odinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM)systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1),(2+1) and(3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers of Zhejiang Agricultural and Forestry University, China (Grant No. 2009RC01)
文摘We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.
文摘The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘By using a simple transformation approach,we solve the higher-order nonlinear Schrödinger equation under another condition.The obtained exact soliton solutions have the following prominent features:The bright soliton can propagate in both the normal and anormal regions;the soliton travelling speed is proportional to its amplitude square;the phase of the soliton is independent of its amplitude or width;and the component solitons of the bound soliton have the same phase.
基金This work is supported by the National Natural Science Foundation of China(Grant No.71690242,No.11731014,No.12001241)the Basic Research Program of Jiangsu Province(Grant No.BK20200885).
文摘In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing transformation with an asymptotic expansion method,the existence and properties of the one-,second-,and third-order RWs for the higher-order nonlinear Schrodinger equation are constructed.In addition,the main characteristics of these solutions are discussed through some graphics,which are draw widespread attention in a variety of complex systems such as optics,Bose-Einstein condensates,capillary fow,superfluidity,fluid dynamics,and finance.In addition,infinitely-many conservation laws are established.
文摘The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.
基金National Natural Science Foundation of China under Grant No.10675065
文摘We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No.10735030)Natural Science Foundation of Zhejiang Province of China (Grant No.Y6090592)+1 种基金Natural Science Foundation of Ningbo City (Grant No.2008A610017)K.C.Wong Magna Fund in Ningbo University
文摘By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.
基金Supported by the National Defense Foundation of China under Grant No.98JS05.4.1.DZ0205.
文摘A newly proposed method,i.e.the adaptive higher-order nonlinear finite impulse response(HONFIR)filter based on higher-order sparse Volterra series expansions,is introduced to predict hyper-chaotic time series.The effectiveness of using adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including Mackey-Glass equation and 4-dimensional nonlinear dynamical system.A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series.Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology (Grant Nos.KJRC2022002 and KJRC2023035)。
文摘When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.
基金supported by the National Natural Sci-ence Foundation of China(Nos.22373091,224B2305,and 22573099).
文摘In this work,we develop an extended dissipaton theory that generalizes the environmental couplings beyond the conventional linear and quadratic forms,enabling the treatment of ar-bitrary order of bath couplings.Ap-plying this theoretical framework to the condensed-phase non-Condon spectroscopy,we demonstrate the in-terplay of anharmonicity,non-Con-don and solvent effects on optical spectra,where the higher-order cou-plings arise from the anharmonicity of nuclear potential surface of the excited state.Precise simulations are carried out with high efficiency on linear absorption spectra involving the above mentioned correlated effects.We exhibit how an anharmonic potential modulates the vibronic feature,offering insights into the role of nonlinear environmental couplings in spectroscopic signatures and exemplifying the success of the extended dissipaton formalism as an exact and efficient method for higher-or-der bath couplings.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
