On the Integrable Two-Component (2+1)-dimensional Davey-Stewartson Equation I

The geometric-gauge equivalent of the famous Ishimori spin equation is the (2+1)-dimensional Davy-Stewartson equation, which in turn is one of the (2+1)-dimensional generalizations of the nonlinear Schrodinger equation. Multicomponent generalization of nonlinear integrable equations attract considerable interest from both physical and mathematical points of view. In this paper, the two-component integrable generalization of the (2+1)-dimensional Davy-Stewartson I equation is obtained based on its one-component representation, and the corresponding Lax representation is also obtained.