%0 Journal Article
%T Energy cascades for NLS on the torus
%A Remi Carles
%A Erwan Faou
%J Mathematics
%D 2010
%I arXiv
%X We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system.
%U http://arxiv.org/abs/1010.5173v1