@article{d77567a9ad224c279449bdb3f3483872,
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",
note = "Funding Information: The authors are grateful to Jalal Shatah for suggesting the question at the heart of this article, to Herbert Koch for very helpful discussions during the writing of the article, and to Or Hershkovits for his geometric insight. They also warmly thank the referees for their careful reading. P. Germain is partially supported by NSF grant DMS-1101269, a start-up grant from the Courant Institute, and a Sloan fellowship. F. Rousset is partially supported by the ANR projects BoND (ANR-13-BS01-0009-01) and DYFICOLTY (ANR-13-BS01-0003-01). Publisher Copyright: {\textcopyright} European Mathematical Society 2019",
year = "2019",
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",
}