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Traveling wave solutions of the Schrödinger map equation

✍ Scribed by Fanghua Lin; Juncheng Wei

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
286 KB
Volume
63
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

We first construct traveling wave solutions for the Schrödinger map in ℝ^2^

of the form m(x~1~, x~2~ − ϵ t), where m has exactly two vortices at approximately
$\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}(\pm {{1}\over{2 \epsilon}}, 0) \in \R^2$
of degree ±1. We use a perturbative approach that gives a complete characterization of the asymptotic behavior of the solutions. With a few modifications, a similar construction yields traveling wave solutions of Schrödinger map equations in higher dimensions. © 2010 Wiley Periodicals, Inc.

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