一类辅助微分方程的亚纯解及其应用

Meromorphic solutions of a class of auxiliary differential equation and its applications

介绍了寻求非线性偏微分方程精确解的方法--复方法,用该方法研究了一类辅助微分方程的亚纯解,并将所得结果运用于寻求相关的非线性偏微分方程的精确解,得到Vakhnenko-Parkes方程和Dodd-Bullough-Mikhailov方程的精确解。

This paper introduce a method to find exact solutions of nonlinear partial differential equations-complex method, and derive meromorphic solutions for a class of algebraic differential equation by the mentioned method. The results are used to seek exact solutions of nonlinear differential equations. Exact solutions of the Vakhnenko-Parkes equation and Dodd-Bullough-Mikhailov equation are obtained.