Soliton asymptotics for KdV shock waves via classical inverse scattering
Analysis of PDEs
2021-09-20 v1 Exactly Solvable and Integrable Systems
Abstract
We show how the inverse scattering transform can be used as a convenient tool to derive the long-time asymptotics of shock waves for the Korteweg-de Vries (KdV) equation 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.
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Cite
@article{arxiv.2109.08423,
title = {Soliton asymptotics for KdV shock waves via classical inverse scattering},
author = {Iryna Egorova and Johanna Michor and Gerald Teschl},
journal= {arXiv preprint arXiv:2109.08423},
year = {2021}
}
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22 pages