Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves

Frédéric Chardard

doi:10.1016/j.crma.2007.11.003

Dynamical Systems

Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves
[Un indice de Maslov pour les ondes solitaires obtenu comme limite de l'indice de Maslov pour les ondes périodiques]

Présenté par : Gérard Iooss

Frédéric Chardard ¹

¹ CMLA, ENS Cachan, CNRS, UniverSud, 61 Avenue President Wilson, F-94230 Cachan, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 689-694.

Résumé
Abstract

On peut définir l'indice de Maslov pour une onde solitaire en approchant l'onde solitaire par des ondes périodiques : lorsqu'une suite d'ondes périodiques $ϕ^{α}$ converge vers l'onde solitaire ϕ, alors sa limite peut-être utilisée comme définition de l'indice de Maslov de ϕ.

A Maslov index for a solitary wave can be defined by approximating the solitary wave with periodic waves: when a sequence of periodic waves $ϕ^{α}$ converges to the solitary wave ϕ, then the sequence of Maslov indices converges and its limit can be used as a definition for the Maslov index of ϕ.

Reçu le : 2007-07-12
Accepté le : 2007-10-31
Publié le : 2007-11-28

DOI : 10.1016/j.crma.2007.11.003

Affiliations des auteurs :

Frédéric Chardard ¹

¹ CMLA, ENS Cachan, CNRS, UniverSud, 61 Avenue President Wilson, F-94230 Cachan, France

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     author = {Fr\'ed\'eric Chardard},
     title = {Maslov index for solitary waves obtained as a limit of the {Maslov} index for periodic waves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {689--694},
     publisher = {Elsevier},
     volume = {345},
     number = {12},
     year = {2007},
     doi = {10.1016/j.crma.2007.11.003},
     language = {en},
}

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Frédéric Chardard. Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves. Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 689-694. doi : 10.1016/j.crma.2007.11.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.003/

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