Interactions and Asymptotics of Dispersive Shock Waves -- Korteweg-de Vries Equation
Pattern Formation and Solitons
2015-06-12 v1 Exactly Solvable and Integrable Systems
Abstract
The long-time asymptotic solution of the Korteweg-de Vries equation for general, step-like initial data is analyzed. Each sub-step in well-separated, multi-step data forms its own single dispersive shock wave (DSW); at intermediate times these DSWs interact and develop multiphase dynamics. Using the inverse scattering transform and matched-asymptotic analysis it is shown that the DSWs merge to form a single-phase DSW, which is the `largest' one possible for the boundary data. This is similar to interacting viscous shock waves (VSW) that are modeled with Burgers' equation, where only the single, largest-possible VSW remains after a long time.
Keywords
Cite
@article{arxiv.1301.1032,
title = {Interactions and Asymptotics of Dispersive Shock Waves -- Korteweg-de Vries Equation},
author = {Mark J. Ablowitz and Douglas E. Baldwin},
journal= {arXiv preprint arXiv:1301.1032},
year = {2015}
}
Comments
5 pages, 3 figures