Author: Guido Gentile and Vieri Mastropietro

Title: Construction of periodic solutions of the nonlinear wave equation under strong irrationality conditions by the Lindstedt series method
 
Abstract: We prove the existence of oscillatory solutions of the nonlinear wave equation, under irrationality conditions stronger than the usual Diophantine one, by perturbative techniques inspired by the Lindstedt series method originally introduced in classical mechanics to study the existence of invariant tori in quasi-integrable Hamiltonian systems.

Keywords: Nonlinear wave equation; Periodic solutions; Lindstedt series method; Tree formalism; Perturbation theory.

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

Vieri Mastropietro
Dipartimento di Matematica
Università di Roma ``Tor Vergata"
Via della Ricerca Scientifica, Italy
e-mail: mastropi@mat.uniroma2.it