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

作　　者：沙安 李连忠 SHA An;LI Lianzhong(School of Science,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《应用数学》2018年第4期890-897,共8页Mathematica Applicata

基　　金：Supported by the Jiangsu Province Natural Science Foundation of China Youth Fund(BK20170171)

摘　　要：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.

关 键 词：广义变系数mKdV方程 BACKLUND变换 Painleve检验 幂级数法 精确解 

分 类 号：O175[理学—数学]