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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.