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 Schrödinger 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 Schrödinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.

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

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

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