Rarefaction waves for the Toda equation via nonlinear steepest descent

Iryna Egorova; Johanna Michor; Gerald Teschl

doi:10.3934/dcds.2018081

Article Contents

2018, Volume 38, Issue 4: 2007-2028. Doi: 10.3934/dcds.2018081

This issue Previous Article Large deviations for stochastic heat equations with memory driven by Lévy-type noise Next Article Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems

Rarefaction waves for the Toda equation via nonlinear steepest descent

1.
B. Verkin Institute for Low Temperature Physics and Engineering, 47, Nauky ave, 61103 Kharkiv, Ukraine
2.
V.N. Karazin Kharkiv National University, 4, Svobody sq. 61022 Kharkiv, Ukraine
3.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1,1090 Wien, Austria
4.
Erwin Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9,1090 Wien, Austria

Received: January 2017

Revised: November 2017

Published: July 2018

Research supported by the Austrian Science Fund (FWF) under Grant No. V120.

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Abstract

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice with steplike initial data corresponding to a rarefaction wave.

Keywords:

Toda equation.

Mathematics Subject Classification: Primary: 37K40, 35Q53; Secondary: 37K45, 35Q15.

Citation:

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Figure 1. Toda rarefaction problem with non-overlapping background spectra $\sigma(H_{\ell})=[1.2, 2.8]$, $\sigma(H_r)=[-1,1]$; $a=0.4$, $b=2$

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Figure 2. Signature table for $g(z)$

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Figure 3. Contour deformation of Step 2

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