Long wave limit for Schrodinger maps

TL;DR

This paper investigates the long wave limits of Schrödinger maps into Kähler manifolds, deriving KdV-type systems and applying the theory to models like Gross-Pitaevskii and Landau-Lifshitz equations.

Contribution

It develops a general framework for long wave limits of Schrödinger maps into Kähler manifolds and applies it to important physical models.

Findings

Derivation of KdV-type systems from Schrödinger maps

Application to Gross-Pitaevskii equation

Application to Landau-Lifshitz systems

Abstract

We study long wave limits for general Schrodinger maps systems into Kahler 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 limit of the Gross-Pitaevskii equation, and of the Landau-Lifshitz systems for ferromagnetic and antiferromagnetic chains.