Premium
Traveling wave solutions of the Schrödinger map equation
Author(s) -
Lin Fanghua,
Wei Juncheng
Publication year - 2010
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20338
Subject(s) - traveling wave , mathematics , vortex , mathematical physics , schrödinger's cat , schrödinger equation , mathematical analysis , construct (python library) , degree (music) , physics , meteorology , computer science , acoustics , programming language
We first construct traveling wave solutions for the Schrödinger map in ℝ 2$\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}{{\partial m}\over{\partial t}}= m \times (\Delta m - m_3{\vec{e}}_3) \quad {\rm in} \;\R^2 \times \R $ 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.