Long wave limit for Schrödinger maps

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.