JournalsjemsVol. 21, No. 8pp. 2517–2602

Long wave limit for Schrödinger maps

  • Pierre Germain

    New York University, New York, USA
  • Frédéric Rousset

    Université Paris-Sud, Orsay, France and Institut Universitaire de France
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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.

Cite this article

Pierre Germain, Frédéric Rousset, Long wave limit for Schrödinger maps. J. Eur. Math. Soc. 21 (2019), no. 8, pp. 2517–2602

DOI 10.4171/JEMS/888