Zhiber-Shabat方程的精确行波解

摘要

采用Fan子方程法并借助符号计算软件Maple求解Zhiber-Shabat方程,利用平衡法求得Fan子方程的参数约束条件,得出在不同参数条件下子方程解的显式表达式,进而获得了原方程丰富的精确行波解,得到几类具有代表性的行波解,包括三角函数解、双曲函数解、双周期Jacobi椭圆函数解.%In this letter, the Fan sub-equation method is used to construct traveling wave solutions of the Zhiber-Shabat equation with the aid of software Maple. By using the balance method we can get the condition of parameters of the sub-equation and the solutions of it under different parameter conditions, then some exact solutions of the Zhiber-Shabat equation are obtained, which include triangular function solutions , hyperbolic function solutions and Jacobi elliptic function solutions with double periodics.