Symmetry and chaos in the complex Ginzburg-Landau equation- I.Reflectional symmetries

摘要

The complex Ginzburg-Landau (CGL) equation on a one-dimensional domain with periodic boundary conditions has a number of different symmetries. Solutions of the CGL equation may or may not be fixed by the action of these symmetries. We investigate the stability of chaotic solution with some reflectional symmetry to perturbations which bear that symmetry. This can be achieved by considering the isotypic decomposition of the space an finding the dominant Lyapunov exponent associated with each isotypic component.