Rendiconti Lincei - Matematica e Applicazioni


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Volume 24, Issue 2, 2013, pp. 199–214
DOI: 10.4171/RLM/652

Published online: 2013-06-26

Existence and stability of quasi-periodic solutions for derivative wave equations

Massimiliano Berti[1], Luca Biasco and Michela Procesi[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) Università di Roma La Sapienza, Italy

In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems.

Keywords: Wave equation, KAM for PDEs, quasi-periodic solutions, small divisors, quasi-Toeplitz property

Berti Massimiliano, Biasco Luca, Procesi Michela: Existence and stability of quasi-periodic solutions for derivative wave equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), 199-214. doi: 10.4171/RLM/652