New general solutions for the general elliptic and auxiliary equations and application to the coupled KdV equation

Abstract

In this article, we first obtain generalized soliton solutions of the general elliptic and auxiliary equations by the Exp-function method. Then by the obtained solutions, we find new and more general solutions of the coupled KdV equation.

Keywords:

• Exp-function method
• general elliptic equation
• auxiliary equation
• sub-equation method
• coupled KdV system

2000 AMS Subject Classification :

• 35C05

Acknowledgements

The authors would like to thank the anonymous referees for their useful comments.