偏微分方程的非线性变换和精确解

Nonlinear Transformations of Partial Differential Equations and Their Exact Solutions

利用截属的Painlev'e展开式、非线性变换和可积的微分方程，可以求出一类非线性偏微分方程的自Backlund变换和它的精确解，孤立波解。波动方程、Hirota-Satsuma方程组和非线性色散与耗散方程作为例子来说明这一方法。

Using truncated Painlev' e expansion, nonlinear transformation, and integrable differential equation, we obtain Backlund transformation and the exact solutions of a kind of partial differential equations. Wave equation, Hiro-ta - Satsuma equation, nonlinear chromatic dispersion and dissipation equation are discussed to illustrate this method.