Variable-coefficient auxiliary equation method for exact solutions of non-linear evolution equations

Abstract

In this paper, a variable-coefficient auxiliary equation method is proposed to seek more general exact solutions of non-linear evolution equations. Being concise and straightforward, this method is applied to the Kawahara equation, Sawada–Kotera equation and (2+1)-dimensional Korteweg–de Vries equations. As a result, many new and more general exact solutions are obtained including Jacobi elliptic, hyperbolic and trigonometric function solutions. It is shown that the proposed method provides a straightforward and effective method for non-linear evolution equations in mathematical physics.

Keywords:

• non-linear evolution equations
• variable-coefficient auxiliary equation method
• Jacobi elliptic function solutions
• hyperbolic function solutions
• trigonometric function solutions

2000 AMS Subject Classification :

• 35Q51
• 35Q53
• 35Q99

Acknowledgements

The author would like to express his sincere thanks to the referees for their valuable suggestions and comments. This work was supported by the Natural Science Foundation of Educational Committee of Liaoning Province of China under Grant No. 20060022.