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

Abstract

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].