Integral bifurcation method combined with computer for solving a higher order wave equation of KdV type

Abstract

In this paper, the integral bifurcation method combined with computer methods was used to study a higher order wave equation of KdV type. Under different parameter conditions, many integral bifurcations are obtained. By these integral bifurcations, using the software Maple, we have obtained many exact travelling wave solutions such as periodic soliton solutions and periodic cusp wave solutions, solitary wave solutions, and solitary cusp wave solutions.

Keywords:

• integral bifurcation method
• higher order wave equation of KdV type
• periodic cusp wave solution
• periodic soliton solution
• solitary cusp solutions

2000 AMS Subject Classification :

• 35Q51
• 35Q58
• 36K65
• 34A20

Acknowledgements

This research was supported by the Scientific Foundation of Educational Department of Yunnan Province (06Y147A), the Natural Science Foundation of Yunnan Province (2007A080M), and the Natural Science Foundation of China (10571062).