Article
J. Math. Anal. Appl. 514, 126251 (2022) [DOI: 10.1016/j.jmaa.2022.126251]

Soliton asymptotics for the KdV shock problem via classical inverse scattering

Iryna Egorova, Johanna Michor, and Gerald Teschl

Abstract
We show how the inverse scattering transform can be used as a convenient tool to derive the long-time asymptotics of the Korteweg-de Vries (KdV) shock problem in the soliton region. In particular, we improve the results previously obtained via the nonlinear steepest decent approach both with respect to the decay of the initial conditions as well as the region where they are valid.

MSC2020: Primary 37K40, 35Q53; Secondary 37K45, 35Q15
Keywords: KdV equation, shock wave, inverse scattering transform, solitons

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