In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete ...In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.展开更多
Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we in...Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.展开更多
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.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 extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonli...In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.展开更多
Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.
By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other ...By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
文摘In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.
文摘Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.
基金Supported by the National Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
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.
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
基金The project supported by National Natural Science Foundation of China under Grant No.40305006the Ministry of Science and Technology of China through Special Public Welfare Project under Grant No.2002DIB20070
文摘In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.
基金The project supported by the National Outstanding Youth Foundation of China (No.19925522)+2 种基金the Research Fund for the Doctoral Program of Higher Education of China (Grant.No.2000024832)National Natural Science Foundation of China (No.90203001)
文摘Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)Supported by the Natural Science Foundation of Henan Province(0111050200)
文摘By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
