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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Kourakis, I., Sultana, S. & Verheest, F. Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation. Astrophys Space Sci 338, 245–249 (2012). https://doi.org/10.1007/s10509-011-0958-5
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DOI: https://doi.org/10.1007/s10509-011-0958-5