On the gauge equivalence of the two-layer M-XCIX equation and the two-component Schr¨odinger-Maxwell-Bloch equation

Abstract

The interest in integrable systems increased with the discovery in the late 1960s of the Inverse scattering problem method, which arose as a result of investigations in plasma physics. M.D. Kruskal and N. Zabusky, investigating the Korteweg-de Vries equation, found by numerical simulation that its exact soliton solutions collide resiliently, which is not typical for linear waves. This served as a new impetus to the development of various methods for solving nonlinear evolution equations, as well as solitons and solutions associated with them. The gauge equivalence of the two-component Schr¨odinger-Maxwell-Bloch equation, the Γ -spin system and the integrable two-layer spin system, the so-called two-layer Myrzakulov-XCIX equation, is proved in this work. These systems of equations are integrable and admit Lax representations. Complete formsfor the Γ -spin system with a self-consistent potential and the two-layer spin system with potentials are established. The Myrzakulov-XCIX equation is the soliton equation describing nonlinear magnetization processes in multilayer ferromagnets.