Interactions and Asymptotics of Dispersive Shock Waves -- Korteweg-de Vries Equation

2013/01/06 by Mark J. Ablowitz, Douglas E. Baldwin · 1 citation
Physics and Astronomy · #nlin.PS #nlin.SI

paper · pdf · doi:10.1016/j.physleta.2012.12.040

5 pages, 3 figures

arxiv created 2013/01/06 · arxiv updated 2015/06/12

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.

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