On the influence of the discrete spectrum and resonances on the asymptotics of the Toda shock wave

We rigorously derive and discuss in detail the 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