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

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Keywords

  • KdV equation
  • Long wave limit
  • Schrödinger map

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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