A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions ...In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.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
We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations an...We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation.After substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave solutions.It is shown that these employed methods are more powerful tools for nonlinear wave equations.展开更多
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
文摘In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.
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.
文摘We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation.After substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave solutions.It is shown that these employed methods are more powerful tools for nonlinear wave equations.
