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

The paper deals with the detection and calculation of bifurcation from nontrivial static solutions to rotating wave solutions of the nonlinear evolution equation ∂u/∂t+g(u,α)=0, where g is equivariant with respect to an action of the group O(2)×O(2), α 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.