On the Long-Time Asymptotics for the
Korteweg-de Vries Equation with Steplike
Initial Data Associated with Rarefaction
Waves

K. Andreiev and I. Egorova

B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: kyrylo.andreiev@gmail.com, iraegorova@gmail.com

Received August 15, 2017

Abstract

We discuss an asymptotical behavior of the rarefaction wave for the KdV
equation in the region behind the wave front. The first and the second
terms of the asymptotical expansion for such a solution with respect to large
time were derived without detailed analysis in [1]. In the present work, we
correct the formula for the second term by investigating the corresponding
parametrix problem. We also study an in
uence of the resonance on the
asymptotical behavior of the solution.