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Quasi-periodic oscillations for wave equations under periodic forcing

Massimiliano Berti; Michela Procesi — 2005

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced, nonlinear wave equations with periodic spatial boundary conditions is established. We consider both the cases the forcing frequency is (Case A) a rational number and (Case B) an irrational number.

KAM theory for the hamiltonian derivative wave equation

Massimiliano Berti; Luca Biasco; Michela Procesi — 2013

Annales scientifiques de l'École Normale Supérieure

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.

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