A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spect...A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux 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 DEW equation such as rational solutions, soliton solutions, periodic solutions.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10871182Innovation Scientists and Technicians Troop Construction Projects of Henan Province
文摘A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux 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 DEW equation such as rational solutions, soliton solutions, periodic solutions.