Long wave limit for Schrödinger maps

Pierre Germain; Frédéric Rousset

doi:10.4171/JEMS/888

Long wave limit for Schrödinger maps

Pierre Germain, Frédéric Rousset

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study long wave limits for general Schrödinger map systems into Kähler manifolds with a constraining potential vanishing on a Lagrangian submanifold. We obtain KdV-type systems set on the tangent space of the submanifold. Our general theory is applied to study the long wave limits of the Gross-Pitaevskii equation and of the Landau-Lifshitz systems for ferromagnetic and anti-ferromagnetic chains.

Original language	English (US)
Pages (from-to)	2517-2602
Number of pages	86
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	8
DOIs	https://doi.org/10.4171/JEMS/888
State	Published - 2019

Keywords

KdV equation
Long wave limit
Schrödinger map

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.4171/JEMS/888

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Cite this

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title = "Long wave limit for Schr{\"o}dinger maps",

abstract = "We study long wave limits for general Schr{\"o}dinger map systems into K{\"a}hler manifolds with a constraining potential vanishing on a Lagrangian submanifold. We obtain KdV-type systems set on the tangent space of the submanifold. Our general theory is applied to study the long wave limits of the Gross-Pitaevskii equation and of the Landau-Lifshitz systems for ferromagnetic and anti-ferromagnetic chains.",

keywords = "KdV equation, Long wave limit, Schr{\"o}dinger map",

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AU - Rousset, Frédéric

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AB - We study long wave limits for general Schrödinger map systems into Kähler manifolds with a constraining potential vanishing on a Lagrangian submanifold. We obtain KdV-type systems set on the tangent space of the submanifold. Our general theory is applied to study the long wave limits of the Gross-Pitaevskii equation and of the Landau-Lifshitz systems for ferromagnetic and anti-ferromagnetic chains.

KW - KdV equation

KW - Long wave limit

KW - Schrödinger map

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