广义CH-DP方程的尖弧立波解

Peaked Solitary Wave Solution to Generalized CH-DP Equation

研究了Camassa-Holm方程和Degasperis-Processi方程广义形式的尖孤立波解.运用微分方程定性理论和动力系统分支方法证明了这一类解的存在性,给出了解的显函数表达式,同时获得了光滑孤立波解的显函数表达式,推广了文献中的某些结果,解决了文献中的一个猜测.

This paper investigates the peaked solitary wave solutions to the generalized forms of the Camassa-Holm equation and the Degasperis-Processi equation. By means of the qualitative theory of differential equations and the bifurcation method of dynamic systems, the existence of the peaked solitary wave solutions is proved, and the ex- plicit expressions of the peaked and the smooth solitary wave solutions are respectively given. Moreover, some resuits in the literature are extended and a conjecture is clarified.