How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave

We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically a finite gap. In particular, we describe the influence of the discrete spectrum in the spectral gap on the shift of the phase in the theta-function representation for this so...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
Hauptverfasser: Egorova, Iryna, Michor, Johanna
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211304
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Zitieren:How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave. Iryna Egorova and Johanna Michor. SIGMA 17 (2021), 045, 32 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Egorova, Iryna
Michor, Johanna
author_facet Egorova, Iryna
Michor, Johanna
citation_txt How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave. Iryna Egorova and Johanna Michor. SIGMA 17 (2021), 045, 32 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically a finite gap. In particular, we describe the influence of the discrete spectrum in the spectral gap on the shift of the phase in the theta-function representation for this solution. We also study the effect of possible resonances at the endpoints of the gap on this phase. This paper is a continuation of research started in [arXiv:2001.05184].
first_indexed 2026-03-19T02:46:08Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-19T02:46:08Z
publishDate 2021
publisher Інститут математики НАН України
record_format dspace
spelling Egorova, Iryna
Michor, Johanna
2025-12-29T11:06:38Z
2021
How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave. Iryna Egorova and Johanna Michor. SIGMA 17 (2021), 045, 32 pages
1815-0659
2020 Mathematics Subject Classification: 37K40; 35Q53; 37K45; 35Q15
arXiv:2012.12371
https://nasplib.isofts.kiev.ua/handle/123456789/211304
https://doi.org/10.3842/SIGMA.2021.045
We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically a finite gap. In particular, we describe the influence of the discrete spectrum in the spectral gap on the shift of the phase in the theta-function representation for this solution. We also study the effect of possible resonances at the endpoints of the gap on this phase. This paper is a continuation of research started in [arXiv:2001.05184].
This research was supported by the Austrian Science Fund (FWF) under Grant No. P31651. We thank the referees for their careful reading and their recommendations.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
Article
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spellingShingle How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
Egorova, Iryna
Michor, Johanna
title How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
title_full How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
title_fullStr How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
title_full_unstemmed How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
title_short How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
title_sort how discrete spectrum and resonances influence the asymptotics of the toda shock wave
url https://nasplib.isofts.kiev.ua/handle/123456789/211304
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