Convergence of Lindstedt series for the non linear wave equation

G. Gentile; V. Mastropietro

doi:10.3934/cpaa.2004.3.509

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2004, Volume 3, Issue 3: 509-514. Doi: 10.3934/cpaa.2004.3.509

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Convergence of Lindstedt series for the non linear wave equation

G. Gentile^1, and
V. Mastropietro^2,

1.
Dipartimento di Matematica, Università di Roma Tre, Roma, I-00146
2.
Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma, I-00133

Received: August 31, 2003

Revised: December 31, 2003

Published: August 2004

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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,
Diophantine and irrationality conditions,
Dirichlet boundary conditions.

Mathematics Subject Classification: 35B10, 35B32, 35L70, 47H15, 47N20, 58F27, 58F39.

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