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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https://hal.archives-ouvertes.fr/hal-01954762
Contributor : Philippe Gravejat <>
Submitted on : Thursday, December 13, 2018 - 10:05:05 PM
Last modification on : Friday, April 19, 2019 - 4:54:52 PM
Long-term archiving on : Thursday, March 14, 2019 - 4:21:09 PM

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  • HAL Id : hal-01954762, version 1
  • ARXIV : 1812.05854

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André de Laire, Philippe Gravejat. The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy. 2018. ⟨hal-01954762⟩

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