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Journal Articles Revista Matemática Iberoamericana Year : 2021

The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy

Abstract

We pursue our work on the asymptotic regimes of the Landau-Lifshitz equation for bi-axial ferromagnets. We put the focus on the cubic Schrödinger equation, which is known to describe the dynamics in a regime of strong easy-axis anisotropy. In any dimension, we rigorously prove this claim for solutions with sufficient regularity. In this regime, we additionally classify the one-dimensional solitons of the Landau-Lifshitz equation and quantify their convergence towards the solitons of the one-dimensional cubic Schrödinger equation.
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Dates and versions

hal-01954762 , version 1 (13-12-2018)

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André de Laire, Philippe Gravejat. The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy. Revista Matemática Iberoamericana, 2021, 37 (1), pp.95-128. ⟨10.4171/rmi/1202⟩. ⟨hal-01954762⟩
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