一类广义变系数mKdV方程的Bcklund变换,Painlev检验及精确解（英文）

Bcklund Transformation, Painlev Test and Exact Solutions for a Generalized Variable Coefficient mKdV Equation

本文研究一类广义变系数mKdV方程,基于齐次平衡法,对方程进行Bcklund变换,进而得到方程的精确解;对方程进行Painlev检验,证明方程的可积性.利用推广的CK方法,将广义变系数mKdV方程化为常系数方程,结合幂级数法得到方程的幂级数解.

In this paper, we consider a generalized mKdV equation with variable coefficients. Based on balance homogenous principle, the exact solutions of the equation are given through Bcklund transformation. Then the Painlev test is performed to prove it＇s integrability. At last, we use the CK simplified method to transform the generalized variable coefficient mKdV equation into a constant coefficient equation, and the power series solution is obtained by using the power series method.