O437 94031890非线性 Schrodinger 方程和 Sine Gordon 方程的行波解法=Travelling wave solutions to the non-linear Schr(?)dinger and Sine—Gordon equa-tions[刊,中]/唐世敏(北京大学力学系)∥量子电子学.—1993,10(4).
As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are di...Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.展开更多
Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show t...The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.展开更多
In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the （2＋1）-dimensional Kaup-Kupershmidt （KK） equation are presented. We successfully obtain more genera...In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the （2＋1）-dimensional Kaup-Kupershmidt （KK） equation are presented. We successfully obtain more general exact travelling wave solutions for （2＋ 1）-dimensional KK equation by the symmetry method and the （G1/G）-expansion method. Consequently, we find some new solutions of （2＋1）-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions.展开更多
A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wav...A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.展开更多
A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic functio...A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.展开更多
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions...The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.展开更多
The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensio...The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.展开更多
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speed...The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.展开更多
文摘O437 94031890非线性 Schrodinger 方程和 Sine Gordon 方程的行波解法=Travelling wave solutions to the non-linear Schr(?)dinger and Sine—Gordon equa-tions[刊,中]/唐世敏(北京大学力学系)∥量子电子学.—1993,10(4).
文摘As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
基金The project supported by Scientific Research Fund of Education Department of Heilongjiang Province of China under Grant No.11511008
文摘Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.
基金The project supported by Scientific Research Fund of Heilongjiang Province of China under Grant No. 11511008The author would like to thank referees for their valuable suggestions.
文摘Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
文摘The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.
基金Supported by the Natural Science Foundation of Shandong Province in China under Grant No.Q2005A01
文摘In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the （2＋1）-dimensional Kaup-Kupershmidt （KK） equation are presented. We successfully obtain more general exact travelling wave solutions for （2＋ 1）-dimensional KK equation by the symmetry method and the （G1/G）-expansion method. Consequently, we find some new solutions of （2＋1）-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions.
文摘A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.
基金supported by National Natural Science Foundation of China under Grant No. 10205007the National Natural Science Foundation Gansu Province of China under Grant No. 3zS041-A25-011
文摘A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.
基金The project supported by the Natural Science Foundation of Shandong Province and the Natural Science Foundation of Liaocheng University
文摘The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
基金＊Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R ＆： D Special Fund for Public Welfare Industry （Meteorology） under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission （E03004）
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
文摘The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
文摘The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.
