分数阶长短波演化方程的精确行波解

Exact Travelling Wave Solutions for Fractional Long-Short Wave Evolution Equation

本文运用多项式完全判别系统研究分数阶长短波演化方程,通过行波变换,推导出该方程的精确行波解,包括有理函数解、孤波解、三角函数周期解和椭圆函数周期解,特别是对于椭圆函数周期解,采用其他的方法很难得到.通过设置具体参数,说明了分数阶长短波演化方程的解能够在实际应用中实现.

In this paper,the fractional long-short wave evolution equation is studied by the complete discrimination system for polynomial method.Through the travelling wave transformation,the exact travelling wave solutions of the equation are derived,including rational function solution,solitary wave solution,triangular function periodic solution and elliptic function periodic solution,and especially for the elliptic function periodic solutions,which are difficult to be obtained by other methods.In particular,the concrete parameters are set to show that the solutions of fractional long-short wave evolution equation can be realized in practical application.