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April  2018, 38(4): 2007-2028. doi: 10.3934/dcds.2018081

## 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  January 2018

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

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.

Citation: Iryna Egorova, Johanna Michor, Gerald Teschl. Rarefaction waves for the Toda equation via nonlinear steepest descent. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2007-2028. doi: 10.3934/dcds.2018081
##### References:

show all references

##### References:
Toda rarefaction problem with non-overlapping background spectra $\sigma(H_{\ell})=[1.2, 2.8]$, $\sigma(H_r)=[-1,1]$; $a=0.4$, $b=2$
Signature table for $g(z)$
Contour deformation of Step 2
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