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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     title = {Maslov index for solitary waves obtained as a limit of the {Maslov} index for periodic waves},
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     pages = {689--694},
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     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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[4] F. Chardard, F. Dias, T.J. Bridges, Computing the Maslov index of solitary waves, in preparation

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Frédéric Chardard; Thomas J Bridges Transversality of homoclinic orbits, the Maslov index and the symplectic Evans function, Nonlinearity, Volume 28 (2015) no. 1, p. 77 | DOI:10.1088/0951-7715/28/1/77
Todd Kapitula; Keith Promislow The Evans Function for Sturm–Liouville Operators on the Real Line, Spectral and Dynamical Stability of Nonlinear Waves, Volume 185 (2013), p. 249 | DOI:10.1007/978-1-4614-6995-7_9
Frédéric Chardard; Frédéric Dias; Thomas J. Bridges Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four, Physica D, Volume 240 (2011) no. 17, pp. 1334-1344 | DOI:10.1016/j.physd.2011.05.014 | Zbl:1228.35197
Frédéric Chardard; Frédéric Dias; Thomas J. Bridges Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space, Physica D, Volume 238 (2009) no. 18, pp. 1841-1867 | DOI:10.1016/j.physd.2009.05.008 | Zbl:1179.37097
Frédéric Chardard; Frédéric Dias; Thomas J. Bridges On the Maslov index of multi-pulse homoclinic orbits, Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, Volume 465 (2009) no. 2109, pp. 2897-2910 | DOI:10.1098/rspa.2009.0155 | Zbl:1186.37030

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