BACKLUND TRANSFORMATION AND ANALYTIC SOLUTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES MODEL FROM FLUID DYNAMICS AND PLASMAS

摘要

We investigate a generalized variable-coefficient modified Korteweg-de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Backlund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Backlund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg-de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg-de Vries (vc-cmKdV) equation, respectively.