Abstract:
In this talk I will present a result about the dynamics of a d-dimensional Klein-Gordon lattice with periodic boundary conditions, for d ≤ 3.
If we consider initial data supported on one low-frequency Fourier mode, we can show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schrödinger (NLS) equation.
Exploiting a result by Kuksin about the growth of Sobolev norms for the small-dispersion NLS, we describe an energy cascade phenomenon for the Klein-Gordon lattice, where part of the energy is transferred to modes associated to higher frequencies.
Such a phenomenon holds within the time-scale for which we can ensure the validity of the continuous approximation.
Il seminario avrà luogo presso il Dipartimento di Matematica e Fisica, L.go S. L. Murialdo 1 - Aula 211
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