Camassa-Holm方程和Degasperis-Procesi方程的显式精确解

摘要

In this paper,a new general method,namely,the extended sinh-cosh method,is presen-ted,to seek multiple exact special solutions of nonlinear dispersive partial differential equations.The standard Camassa-Holm equation and the Degasperis-Procesi equation are chosen to illustrate the con-crete scheme of our approach.The peaked solitary wave solutions and new exact solutions with solitary wave patterns are obtained.The fact that a nonlinear dispersive wave equation in compressible elastic rods has no exact special solution with solitary wave patterns like that of the Camassa-Holm equation and the Degasperis-Procesi equation is also given.Some results in the literature can be regarded as special cases of result in this paper.%提出了寻找非线性色散偏微分方程多个精确特解的一种新方法--扩展sinh-cosh方法.选取标准的Camassa-Holm方程和Degasperis-Procesi方程以展示这种方法的具体格式.获得了Camassa-Holm方程和Degas.peris-Procesi方程的尖孤立波解和具孤立波模式的新精确解.给出了一个事实:出现在可压缩弹性杆中的非线性色散波方程没有像Camassa-Holm方程和Degasperis-Procesi方程那样的具孤立波模式的精确解.文献中的结果可以看作本文结果的特例.