Single peak solitary wave solutions for the generalized Camassa–Holm equation

Abstract

This Letter presents all possible smooth, peaked and cusped solitary wave solutions for the generalized Camassa–Holm equation under the inhomogeneous boundary condition.The parametric conditions of existence of the smooth, peaked and cusped solitary wave solutions are given by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for smooth, peaked and cusped solitary wave solutions of the generalized Camassa–Holm equation.

Keywords:

• generalized Camassa–Holm equation
• single peak solitary wave
• solitary wave
• cuspon

AMS Subject Classifications:

• 37k40

Acknowledgments

Useful suggestions and comments made by the referee are gratefully acknowledged. This research was supported by the National Natural Science Foundation of China (11271171/A011701); Natural Science Foundation of Jiangxi Province(20122BAB201013); the Innovative Research Team Support plan of Jiujiang University.