Darboux Transformation and Exact Solutions of the Myrzakulov-Lakshmanan-II Equation

TL;DR

This paper constructs Darboux transformations for the integrable (2+1)-dimensional ML-II equation, enabling explicit derivation of its 1-soliton and 2-soliton solutions, advancing understanding of its integrable structure.

Contribution

The paper develops a Darboux transformation method for the ML-II equation and derives explicit soliton solutions, which is a novel analytical approach for this equation.

Findings

Explicit 1-soliton solutions derived

Explicit 2-soliton solutions derived

Demonstrates integrability via Darboux transformation

Abstract

The Myrzakulov-Lakshmanan-II (ML-II) equation is one of a (2+1)-dimensional generalizations of the Heisenberg ferromagnetic equation. It is integrable and has a non-isospectral Lax representation. In this paper, the Darboux transformation (DT) for the ML-II equation is constructed. Using the DT, the 1-soliton and 2-soliton solutions of the ML-II equation are presented.