GAUGE EQUIVALENCE BETWEEN THE Г-SPIN SYSTEM AND (2+1)-DIMENSIONAL TWO-COMPONENT NONLINEAR SCHRODINGER EQUATION

Аннотация

At present, the question of studying multidimensional nonlinear evolution equations in the framework of the theory of solitons is very relevant. Their usefulness is confirmed by numerous scientific publications, articles and many international conferences. One of the results of these works is the conclusion that, each (1+1)-dimensional soliton equation corresponds to several (2+1)-dimensional integrable and nonintegrable extensions. This led to the intensive development of an important subclass of nonlinear evolution equations of the theory of integrable spin systems. The simplest example of an integrable spin system is the equation Myrzakulov-I (M-I). The M-I equation is a (2+1)-dimensional integrable generalization of the well-known Landau-Lifshitz equation and for y = x it is reduced to it. In this paper, we consider the Г-spin system. This spin system corresponds to the 2-layer M-I equation. A matrix Lax representation for the aforementioned spin system in symmetric space is proposed. The main result of this work is the establishment of gauge equivalence between the Γ-spin system and the (2+1)-dimensional two-component non-linear Schrödinger equation.