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

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

2011-12-06

arxiv.org/abs/1112.1285v1

Astrophys. Space Sci. 338 (2012) 245-249

Physics

Space Physics

Accepted for publication in Astrophysics & Space Science

Scientific paper

10.1007/s10509-011-0958-5

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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