Abstract
In recent years, multidimensional nonlinear evolutionary equations have been actively studied within the framework of the theory of solitons. Their relevance is confirmed by numerous scientific publications. In this work the gauge equivalence between the (2+1)-dimensional integrable two-component Davey-Stewartson I (DSI) equation and the Г - spin system is established. Multicomponent generalizations of nonlinear integrable equations are of current interest from both physical and mathematical points of view. In the theory of integrable (soliton) equations, one of the key models is integrable nonlinear Schrodinger-type (NLS) equations. A two-component integrable generalization of the (2+1)-dimensional DSI equation, obtained on the basis of its one-component representation, and its corresponding Lax representation were proposed. A geometric connection between the twolayer spin system and the integrable two-component Manakov system is found. The nonlinear equations are integrated using the inverse scattering problem method by means of a linear system. For each integrable nonlinear equation, as is known, there is a Lax pair of two linear equations, a compatibility condition, that is, a condition of zero curvature, which this equation serves. We have obtained Lax pair whose zero curvature condition gives the Г - spin system.