非线性波方程尖峰孤子解的一种简便求法及其应用

A simple method for solving nonlinear wave equations for their peaked soliton solutions and its application

根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.

According to the characteristics of peaked soliton solution, the undetermined coefficient method for solving nonlinear wave equations for their peaked soliton solutions is submitted and by means of the method several kinds of peaked soliton solutions are obtained for five nonlinear wave equations： the Camassa-Holm, fifth -order KdV-like, generalized Ostrovsky, combined KdV-mKdV and Klein-Gordon equations. The solutions given in literature about Camassa-Holm equation become the special cases of the solutions in this paper. The graphs of some solutions are given through numerical simulation. The special conditions under which the wave equation will have peaked soliton solution is briefly described. The method used in this paper can also be used for solving many other nonlinear equations.