Comptes Rendus
Mathematical analysis/Partial differential equations
Quasi-periodic solutions for nonlinear wave equations
Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 601-604.

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.

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.

Published online:
DOI: 10.1016/j.crma.2015.04.014

Wei-Min Wang 1

1 CNRS and Department of Mathematics, Université Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France
     author = {Wei-Min Wang},
     title = {Quasi-periodic solutions for nonlinear wave equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {601--604},
     publisher = {Elsevier},
     volume = {353},
     number = {7},
     year = {2015},
     doi = {10.1016/j.crma.2015.04.014},
     language = {en},
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PB  - Elsevier
DO  - 10.1016/j.crma.2015.04.014
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%T Quasi-periodic solutions for nonlinear wave equations
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Wei-Min Wang. Quasi-periodic solutions for nonlinear wave equations. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 601-604. doi : 10.1016/j.crma.2015.04.014.

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