Travelling waves and dispersion relation in the spatial unfolding of a periodic orbit

Abstract

For a partial differential equation in spatial dimension one, admitting a spatially homogeneous time periodic solution, we show the generic existence, close to this solution, of a one-parameter family of travelling waves parametrized by their wave number k ( k=0 corresponding to the spatially homogeneous initial solution). The argument is elementary and relies on a direct application of singular perturbation theory (Fenichel's global center manifold theorem). To cite this article: E. Risler, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 833–838.