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arXiv · 1812.05854

The cubic Schr{\"o}dinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy

André De Laire·Philippe Gravejat
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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 Schr{\"o}dinger 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 Schr{\"o}dinger equation.

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André De Laire, Philippe Gravejat. 2018-12-14. The cubic Schr{\"o}dinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy. https://arxiv.org/abs/1812.05854

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