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 |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211304 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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| _version_ | 1862706721839906816 |
|---|---|
| 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].
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| first_indexed | 2026-03-19T02:46:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211304 |
| 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. en 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 published earlier |
| 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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