The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelch...The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtainedincluding solitary wave solutions,trigonometric function solutions and Jacobi elliptic doubly periodic function solutions,some of which are new exact solutions that we have never seen before within our knowledge.The method can be appliedto other nonlinear evolution equations in mathematical physics.展开更多
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper...Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10672053the Scientific Research Fund of the Education Department of Hunan Province under Grant No.07D064
文摘The sinh-Gordon equation expansion method is further extended by generalizing the sinh-Gordon equa-tion and constructing new ansatz solution of the considered equation.As its application,the (2+1)-dimensionalKonopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtainedincluding solitary wave solutions,trigonometric function solutions and Jacobi elliptic doubly periodic function solutions,some of which are new exact solutions that we have never seen before within our knowledge.The method can be appliedto other nonlinear evolution equations in mathematical physics.
基金Project supported by the Science and Technology Foundation of Guizhou Province,China (Grant No 20072009)
文摘Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.
基金supported by National Natural Science Foundation of China(No.11371267 and 11571245)Basic Project of Sichuan Provincial Science and Technology Department(No.2016JY0204)~~
