解的移植法与含源耦合VCmKdV方程的解

根据变系数modified Korteweg-de Vries（VCmKdV）方程与常系数KdV-mKdV方程的非线性项、色散项的相似性，对解已知的KdV-mKdV方程做适当变换，并将它的解移植到解未知的VCmKdV方程，由此构造出两个不同方程解之间的移植关系.利用这种解的移植方法，求得了由两层流体模型经演化获得的含有源（或汇）耦合VCmKdV系统新的精确解和类孤波解.对Bcklund变换与解的移植法进行了比较，分析了源和汇对波幅的影响. 关键词： 解的移植法 KdV-mKdV方程 耦合VCmKdV系统 类孤波解

Transplantation method of solutions and the solutions of a coupled VCmKdV equation with source

According to the comparability of the nonlinear terms and dispersion terms between the variable coefficient modified Korteweg-de Vries （VCmKdV） equation and constant coefficient KdV-mKdV equation, we transform properly the KdV-mKdV equation with known solutions, transplant its solutions to the VCmKdV equation with unknown solutions, and thus construct the transplantation relation between the solutions of two different equations. Utilizing this transplantation method of solutions, we obtain new exact solutions and solitary wave-like solutions of the coupled VCmKdV system, which is derived from a two-layer fluid model with source or sink. Then we compare the Bcklund transformation and this transplantation method, and analyse the influence of source and sink on the amplitude.