浅析CH-γ方程中解的求法

Probe into the Solution of CH-γEquation

CH-γ方程是一个非线性的偏微分方程,可以反映流体、光学和声学等体系的运动过程。通过求解CH-γ方程得到各种解析表达式,对揭示各种解之间的关系和尖点问题具有重要的应用价值。本文利用W·Rui提出的采用Jacobi椭圆函数积分对积分分支法进行改进,然后应用于求解CH-γ方程。在不同的参数条件下,结合Jacobi椭圆函数积分,对CH-γ方程进行约化处理,最终获得了CH-γ方程的纽子波解、反纽子波解、周期波解、孤立波解等行波解和一种显示解,为CH-γ方程的实际问题应用提供参考依据。

The CH-γequation is a nonlinear partial differential equation which reflect the motion process of fluid,optics,and acoustic systems.By solving the CH-γequation,various analytical expressions are obtained,it has important application value for revealing the relationship between various solutions and the cusp problem.This paper makes use of the Jacobi elliptic function integration proposed by W.Rui to improve the integration branch method,and then it is applied in the solution of CH-γequation.Under different parameter conditions,integrated with Jacobi elliptic function integration,the CH-γequation is reduced,and finally the new wave solution,inverse new wave solution,periodic wave solution and solitary wave solution of the CH-γequation are obtained.The traveling wave solution and a display solution provide a reference for the practical application of the CH-γequation.