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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 045, 32 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.045 (Mi sigma1728) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

Iryna Egorovaa, Johanna Michorb

a B. Verkin Institute for Low Temperature Physics and Engineering, 47, Nauky Ave., 61103 Kharkiv, Ukraine
b Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
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DOI: https://doi.org/10.3842/SIGMA.2021.045
Abstract: We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically 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].
Keywords: Toda equation, Riemann–Hilbert problem, steplike, shock.
Funding agency Grant number
Austrian Science Fund P31651
This research was supported by the Austrian Science Fund (FWF) under Grant No. P31651.
Received: January 21, 2021; in final form April 26, 2021; Published online May 1, 2021
Bibliographic databases:
Document Type: Article
MSC: 37K40, 35Q53, 37K45, 35Q15
Language: English
Citation: Iryna Egorova, Johanna Michor, “How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave”, SIGMA, 17 (2021), 045, 32 pp.
Citation in format AMSBIB
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