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arXiv · 1112.1285

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

Ioannis Kourakis·Sharmin Sultana·Frank Verheest
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Abstract

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

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Ioannis Kourakis, Sharmin Sultana, Frank Verheest. 2011-12-06. Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation. https://doi.org/10.1007/s10509-011-0958-5

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