How discrete spectrum and resonances influence the asymptotics of the Toda shock wave
I. Egorova and J. Michor
Keywords: Toda equation, Riemann-Hilbert problem, steplike, Shock.
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 here.
MSC: Primary 37K40, 35Q53; Secondary 37K45, 35Q15.
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