The cubic Schr "odinger regime of the Landau-Lifshitz equation with a\n strong easy-axis anisotropy

2018/12/14 by André de Laire, De Laire, André, Philippe Gravejat +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1812.05854

openalex publication_date 2018/12/14 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

We pursue our work on the asymptotic regimes of the Landau-Lifshitz equation\nfor bi-axial ferromagnets. We put the focus on the cubic Schr "odinger\nequation, which is known to describe the dynamics in a regime of strong\neasy-axis anisotropy. In any dimension, we rigorously prove this claim for\nsolutions with sufficient regularity. In this regime, we additionally classify\nthe one-dimensional solitons of the Landau-Lifshitz equation and quantify their\nconvergence towards the solitons of the one-dimensional cubic Schr "odinger\nequation.\n

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