Abstract and Applied Analysis
Volume 2012 (2012), Article ID 560975, 19 pages
http://dx.doi.org/10.1155/2012/560975
Research Article

Bifurcations of Nonconstant Solutions of the Ginzburg-Landau Equation

Norimichi Hirano1 and Sławomir Rybicki2

1Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, 156 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
2Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Street Chopina 12/18, 87-100 Torun, Poland

Received 24 February 2012; Revised 25 April 2012; Accepted 9 May 2012

Academic Editor: Victor M. Perez Garcia

Copyright © 2012 Norimichi Hirano and Sławomir Rybicki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study local and global bifurcations of nonconstant solutions of the Ginzburg-Landau equation from the families of constant ones. As the topological tools we use the equivariant Conley index and the degree for equivariant gradient maps.