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Energy cascades for NLS on the torus

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  • We consider the nonlinear Schrödinger 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.
    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35C20, 37K55.


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