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arXiv · 1406.0720

Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra

Iryna Egorova·Johanna Michor·Gerald Teschl
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Abstract

We derive the long-time asymptotics for the Toda shock problem using the nonlinear steepest descent analysis for oscillatory Riemann--Hilbert factorization problems. We show that the half plane of space/time variables splits into five main regions: The two regions far outside where the solution is close to free backgrounds. The middle region, where the solution can be asymptotically described by a two band solution, and two regions separating them, where the solution is asymptotically given by a slowly modulated two band solution. In particular, the form of this solution in the separating regions verifies a conjecture from Venakides, Deift, and Oba from 1991.

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Iryna Egorova, Johanna Michor, Gerald Teschl. 2014-06-03. Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra. https://doi.org/10.15407/mag14.04.406

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