Symmetry-breaking bifurcation in O(2) x O(2)-symmetric nonlinear large problems and its application to the Kuramoto-Sivashinsky equation in two spatial dimensions

摘要

The paper deals with the detection and calculation of bifurcation from nontrivial static solutions to rotating wave solutions of the nonlinear evolution equation partial derivativeu/partial derivativet + g(u, alpha) = 0, where g is equivariant with respect to an action of the group O(2) x O(2), alpha is a bifurcation parameter. The method and technique derived here is applied to the nonlocal Kuramoto-Sivashinsky (K-S) equation in two spatial dimensions. The bifurcation point to rotating waves is numerically determined, where the rotating wave solution branch is bifurcated, and the original reflectional symmetry is broken. (C) 2004 Elsevier Ltd. All rights reserved.