(2+1) Dimensional Soliton Equations Covariant with respect to the Binary Darboux Transformation

Abstract

Recently we presented (2+1) dimensional soliton equations covariant with respect to the Darboux transformation, including the Davey-Stewartson (DS) -II equation, the Ishimori-II equation and so on. In this paper we introduce the binary Darboux transformation in a auxiliary linear system and derive systematically (2+1) dimensional soliton equations covariant with respect to the binary Darboux transformation, which include not only the DS-I equation and the Ishimori-I equation but also a (2+1) gemeralization of the modified K-dV equation and so on.