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arXiv · 1301.1032

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

Mark J. Ablowitz·Douglas E. Baldwin
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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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Mark J. Ablowitz, Douglas E. Baldwin. 2013-01-06. Interactions and Asymptotics of Dispersive Shock Waves -- Korteweg-de Vries Equation. https://doi.org/10.1016/j.physleta.2012.12.040

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