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KAM for beating solutions of the quintic NLS (1609.01684v1)
Published 6 Sep 2016 in math.AP and math.DS
Abstract: We consider the nonlinear Schr\"{o}dinger equation of degree five on the circle $\mathbb{S}1 = \mathbb{R}/2\pi$. We prove the existence of quasi-periodic solutions which bifurcate from "resonant" solutions (studied in [14]) of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect.