We consider the nonlinear Schrodinger equation in higher dimension with Dirichlet boundary conditions and with a nonlocal smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In certain cases such solutions at leading order are wave packets. The main diffculty in the proof consists in solving a small divisor problem which we do by using a renormalization group approach.

Periodic solutions for the Schrodinger equation with nonlocal smoothing nonlinearities in higher dimension / G., Gentile; Procesi, Michela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 245:(2008), pp. 3253-3326. [10.1016/j.jde.2008.02.037]

Periodic solutions for the Schrodinger equation with nonlocal smoothing nonlinearities in higher dimension

PROCESI, Michela
2008

Abstract

We consider the nonlinear Schrodinger equation in higher dimension with Dirichlet boundary conditions and with a nonlocal smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In certain cases such solutions at leading order are wave packets. The main diffculty in the proof consists in solving a small divisor problem which we do by using a renormalization group approach.
2008
Lindsted series; Hamiltonian PDE's; periodic solutions
01 Pubblicazione su rivista::01a Articolo in rivista
Periodic solutions for the Schrodinger equation with nonlocal smoothing nonlinearities in higher dimension / G., Gentile; Procesi, Michela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 245:(2008), pp. 3253-3326. [10.1016/j.jde.2008.02.037]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/519256
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