We study the completely resonant cubic Nonlinear Schrodinger equation on the torus T^n with n > 2, with the purpose of constructing quasi-periodic solutions with arbitrary m frequencies. We pass to the hamiltonian formalism and perform one step of resonant Birkoff normal form to highlight the relevant part of the non-linearity. We choose appropriately the ``tangential sites'' (from which the quasi-periodic solution bifurcates) so that the new hamiltonian is as simple as possible. This gives rise to a set of geometric and combinatorial constraints on the ``tangential sites'' v_i in Z^n.

Normal form for the completely resonant NLS on the torus T^n / Berti, Massimiliano. - (2010).

Normal form for the completely resonant NLS on the torus T^n

BERTI, MASSIMILIANO
2010

Abstract

We study the completely resonant cubic Nonlinear Schrodinger equation on the torus T^n with n > 2, with the purpose of constructing quasi-periodic solutions with arbitrary m frequencies. We pass to the hamiltonian formalism and perform one step of resonant Birkoff normal form to highlight the relevant part of the non-linearity. We choose appropriately the ``tangential sites'' (from which the quasi-periodic solution bifurcates) so that the new hamiltonian is as simple as possible. This gives rise to a set of geometric and combinatorial constraints on the ``tangential sites'' v_i in Z^n.
2010
Normal form for the completely resonant NLS on the torus T^n / Berti, Massimiliano. - (2010).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/365313
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