Energy cascades for NLS on the torus

Details Energy cascades for NLS on the torus Energy cascades for NLS on the torus

2010-10-25

arxiv.org/abs/1010.5173v1

Mathematics

Analysis of PDEs

15 pages, 2 figures

Scientific paper

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.

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