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How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Iryna Egorova; Johanna Michor. How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a44/

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