Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 4, pp. 325-343   https://doi.org/10.15407/mag13.04.325     ( to contents , go back )
https://doi.org/10.15407/mag13.04.325

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.

Mathematics Subject Classification 2000: 37K40, 35Q53, 35Q15.
Key words: KdV equation, rarefaction wave, parametrix problem.

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