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

André de Laire (1, 2) , Philippe Gravejat (3)

1 Université de Lille
2 Paradyse - Systèmes de particules et systèmes dynamiques
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Mots clés: Nonlinear Schrödinger equation; Asymptotic regimes; Landau-Lifshitz equation

Domaines: Equations aux dérivées partielles [math.AP]

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⟩