On the Stability of Periodic Multi-Solitons of the KdV Equation

In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size [Formula: see text] , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitud...

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Detalles Bibliográficos
Autores principales: Kappeler, Thomas, Montalto, Riccardo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550510/
https://www.ncbi.nlm.nih.gov/pubmed/34776523
http://dx.doi.org/10.1007/s00220-021-04089-9
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author Kappeler, Thomas
Montalto, Riccardo
author_facet Kappeler, Thomas
Montalto, Riccardo
author_sort Kappeler, Thomas
collection PubMed
description In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size [Formula: see text] , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least [Formula: see text] . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE.
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spelling pubmed-85505102021-11-10 On the Stability of Periodic Multi-Solitons of the KdV Equation Kappeler, Thomas Montalto, Riccardo Commun Math Phys Article In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size [Formula: see text] , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least [Formula: see text] . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE. Springer Berlin Heidelberg 2021-05-11 2021 /pmc/articles/PMC8550510/ /pubmed/34776523 http://dx.doi.org/10.1007/s00220-021-04089-9 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Kappeler, Thomas
Montalto, Riccardo
On the Stability of Periodic Multi-Solitons of the KdV Equation
title On the Stability of Periodic Multi-Solitons of the KdV Equation
title_full On the Stability of Periodic Multi-Solitons of the KdV Equation
title_fullStr On the Stability of Periodic Multi-Solitons of the KdV Equation
title_full_unstemmed On the Stability of Periodic Multi-Solitons of the KdV Equation
title_short On the Stability of Periodic Multi-Solitons of the KdV Equation
title_sort on the stability of periodic multi-solitons of the kdv equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550510/
https://www.ncbi.nlm.nih.gov/pubmed/34776523
http://dx.doi.org/10.1007/s00220-021-04089-9
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