GAUGE EQUIVALENCE BETWEEN THE TWO-COMPONENT GENERALIZATION OF THE (2+1)-DIMENSIONAL DAVEY-STEWARTSON I EQUATION AND SPIN SYSTEM

Аннотация

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.