Article

**J. Differential Equations 261, 5371-5410 (2016)**[DOI: 10.1016/j.jde.2016.08.009]

## Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent

### Kyrylo Andreiev, Iryna Egorova, Till Luc Lange, and Gerald Teschl

We apply the method of nonlinear steepest descent to compute the long-time
asymptotics of the Korteweg-de Vries equation with steplike initial data leading to a rarefaction wave.
In addition to the leading asymptotic we also compute the next term in the asymptotic expansion of the
rarefaction wave, which was not known before.

** MSC2000:** Primary 37K40, 35Q53; Secondary 37K45, 35Q15

**Keywords:** *KdV equation, rarefaction wave, Riemann-Hilbert problem*

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