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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Egorova, Iryna, Michor, Johanna
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211304
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave. Iryna Egorova and Johanna Michor. SIGMA 17 (2021), 045, 32 pages

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...