Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinear...

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Detalles Bibliográficos
Autores principales: Geyer, Anna, Pelinovsky, Dmitry E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5633004/
https://www.ncbi.nlm.nih.gov/pubmed/29070918
http://dx.doi.org/10.1007/s11005-017-0941-3
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author Geyer, Anna
Pelinovsky, Dmitry E.
author_facet Geyer, Anna
Pelinovsky, Dmitry E.
author_sort Geyer, Anna
collection PubMed
description We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.
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spelling pubmed-56330042017-10-23 Spectral stability of periodic waves in the generalized reduced Ostrovsky equation Geyer, Anna Pelinovsky, Dmitry E. Lett Math Phys Article We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type. Springer Netherlands 2017-02-02 2017 /pmc/articles/PMC5633004/ /pubmed/29070918 http://dx.doi.org/10.1007/s11005-017-0941-3 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Geyer, Anna
Pelinovsky, Dmitry E.
Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title_full Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title_fullStr Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title_full_unstemmed Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title_short Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
title_sort spectral stability of periodic waves in the generalized reduced ostrovsky equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5633004/
https://www.ncbi.nlm.nih.gov/pubmed/29070918
http://dx.doi.org/10.1007/s11005-017-0941-3
work_keys_str_mv AT geyeranna spectralstabilityofperiodicwavesinthegeneralizedreducedostrovskyequation
AT pelinovskydmitrye spectralstabilityofperiodicwavesinthegeneralizedreducedostrovskyequation

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