Long wave limit for Schrödinger maps

Pierre Germain, Frédéric Rousset

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2517-2602
Number of pages86
JournalJournal of the European Mathematical Society
Volume21
Issue number8
DOIs
StatePublished - Jan 1 2019

Fingerprint

Gross-Pitaevskii Equation
Lagrangian Submanifold
Tangent Space
Type Systems
Korteweg-de Vries Equation
Submanifolds

Keywords

  • KdV equation
  • Long wave limit
  • Schrödinger map

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Long wave limit for Schrödinger maps. / Germain, Pierre; Rousset, Frédéric.

In: Journal of the European Mathematical Society, Vol. 21, No. 8, 01.01.2019, p. 2517-2602.

Research output: Contribution to journalArticle

Germain, Pierre ; Rousset, Frédéric. / Long wave limit for Schrödinger maps. In: Journal of the European Mathematical Society. 2019 ; Vol. 21, No. 8. pp. 2517-2602.
@article{b4ecb2526bb8476589869dbed705e0e0,
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",
author = "Pierre Germain and Fr{\'e}d{\'e}ric Rousset",
year = "2019",
month = "1",
day = "1",
doi = "10.4171/JEMS/888",
language = "English (US)",
volume = "21",
pages = "2517--2602",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society Publishing House",
number = "8",

}

TY - JOUR

T1 - Long wave limit for Schrödinger maps

AU - Germain, Pierre

AU - Rousset, Frédéric

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85068618292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068618292&partnerID=8YFLogxK

U2 - 10.4171/JEMS/888

DO - 10.4171/JEMS/888

M3 - Article

VL - 21

SP - 2517

EP - 2602

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

IS - 8

ER -