Solution asymptotics for the system of Landau–Lifshitz equations under a saddle-node dynamical bifurcation

Abstract

A system of two nonlinear differential equations with slowly varying coefficients is treated. The asymptotics in the small parameter for the solutions that have a narrow transition layer is studied. Such a layer occurs near the moment where the number of roots of the corresponding algebraic system of equations changes. To construct the asymptotics, the matching method involving three scales is used.