2004, 3(3): 509-514. doi: 10.3934/cpaa.2004.3.509

Convergence of Lindstedt series for the non linear wave equation

1. 

Dipartimento di Matematica, Università di Roma Tre, Roma, I-00146

2. 

Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma, I-00133

Received  September 2003 Revised  January 2004 Published  June 2004

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.
Citation: G. Gentile, V. Mastropietro. Convergence of Lindstedt series for the non linear wave equation. Communications on Pure & Applied Analysis, 2004, 3 (3) : 509-514. doi: 10.3934/cpaa.2004.3.509
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