Gauge equivalent structure and solitary wave solution for a modified Landau–Lifshitz equation

• The gauge equivalence between the modified Landau–Lifshitz equation and the perturbed defocusing nonlinear Schrödinger equation is proved.
• Approximate 1-soliton solution to the modified Landau–Lifshitz equation is given.
• Soliton perturbation theory of defocusing nonlinear Schrödinger equation is used to construct the first-order approximate 1-soliton solution to the modified Landau-Lifshitz equation.

In this paper, the gauge equivalence between the modified Landau–Lifshitz equation and the perturbed defocusing nonlinear Schrödinger equation is proved from the perspective of geometry of given curvature condition. By using the gauge equivalence and the soliton perturbation theory of defocusing nonlinear Schrödinger equation, the first-order approximate 1-soliton solution to the modified Landau–Lifshitz equation is given.