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Comptes Rendus Mathématique
Volume 353, n° 7
pages 601-604 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.014
Received : 23 May 2014 ;  accepted : 17 April 2015
Quasi-periodic solutions for nonlinear wave equations
Solutions quasi périodiques pour l'équation des ondes non linéaire
 

Wei-Min Wang
 CNRS and Department of Mathematics, Université Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France 

Abstract

We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This extends the method developed in the limit-elliptic setting in [[12]] to the hyperbolic setting. The additional ingredient is a Diophantine property of algebraic numbers.

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Résumé

On construit des solutions quasi-périodiques en temps pour l'équation des ondes non linéaire sur le tore en dimension quelconque. Tous les résultats précédents se limitent au cercle. Cet article étend la méthode développée pour le cas limite elliptique dans [[12]] au cas hyperbolique. Le nouvel ingrédient est une propriété diophantienne des nombres algébriques.

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