Darboux Transformation and Explicit Solutions for Drinfel'd-Sokolov-Wilson Equation

摘要

A generalized Drinfel'd-Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Darboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DSW equation such as rational solutions, soliton solutions, periodic solutions.