In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equat...In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.展开更多
A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing kno...A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.展开更多
文摘In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
文摘A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.
