(2+1)维变系数方程的Backlund变换与精确解

Backlund Transformation and Exact Solutions for a (2+1)-Dimensional Variable Coefficient Equation

考虑一般的变系数方程,对方程的种子解作适当的未知函数变换,然后利用backlund变换通过演算获得(2+1)维变系数方程的一系列精确解,其中有的解中含有任意函数,当这些任意函数取某些特殊函数时,这些解具有丰富的结构。

Considering the（2＋1） dimensional variable coefficient equation,doing some unknown functions transformation for seed solutions of the equation,we make full use of Backlund transformation and performing mathematical calculations to obtain a series of exact solutions,in which some solution contains arbitrary functions.These solutions posses abundant structures.