FM 10-2008 (arXiv:0804.4365 [math.AP]; mp_arc 08-84)

Author: Guido Gentile and Michela Procesi

Title: Periodic solutions for a class of nonlinear partial differential equations in higher dimension
 
Abstract: We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schr÷dinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinite-dimensional, such as the nonlinear Schr÷dinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.

Keywords: Nonlinear Schr÷dinger equation; Nonlinear wave equation; Nonlinear beam equation; Higher dimension PDEs; Completely resonant equations; Periodic solutions; Renormalisation Group; Tree formalism.

Guido Gentile
Dipartimento di Matematica
UniversitÓ di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it

Michela Procesi
Dipartimento di Matematica
UniversitÓ di Napoli "Federico II"
Via Cinthia, 80126, Napoli, Italy.
e-mail: procesi@dma.unina.it