Compacton-like and kink-like waves for a higher-order wave equation of Korteweg–de Vries type

Abstract

In this paper, the bifurcation method of the dynamical and numerical approach to differential equations to study higher order wave equations of Korteweg–de Vries (KdV) type is used. With this methodology we obtain the compacton-like and kink-like wave solutions of the high order KdV type equation. Their implicit expressions are given and their planar graphs are simulated. The results show that the numerical integrations are identical with the theoretical derivations.

Keywords:

• Compacton-like wave
• Higher order wave equation of KdV type
• Kink-like wave

Acknowledgements

The authors would like to thank Laura Northover for her help in publishing our paper. This research was supported by the Natural Science Foundation of China (10571062), the Science Research Foundation of Yunnan Education Department (5Z0071A) and Natural Science Foundation of Honghe University(XJ1Z0502).