New generalized method to construct new non-travelling wave solutions and travelling wave solutions of K–D equations

Abstract

With the aid of computerized symbolic computation, we obtain new types of general solution of a first-order nonlinear ordinary differential equation with six degrees of freedom and devise a new generalized method and its algorithm, which can be used to construct more new exact solutions of general nonlinear differential equations. The (2+1)-dimensional K–D equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain non-travelling wave solutions and travelling wave solutions.

Keywords:

• generalized algebra method
• (2+1)-dimensional K–D equation
• nonlinear ordinary differential equation
• non-travelling wave solution
• nonlinear partial differential equation

2000 AMS Subject Classification :

• 34–xx
• 35–xx
• 35Dxx
• 35Gxx

Acknowledgements

The authors thank the referee for his/her valuable suggestions. This work has been supported partially by a National Key Basic Research Project of China (2004 CB 318000).