Astrophysics and Space Science

, Volume 338, Issue 2, pp 245–249

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

  • Ioannis Kourakis
  • Sharmin Sultana
  • Frank Verheest

DOI: 10.1007/s10509-011-0958-5

Cite this article as:
Kourakis, I., Sultana, S. & Verheest, F. Astrophys Space Sci (2012) 338: 245. doi: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.


PlasmasShock waves

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Ioannis Kourakis
    • 1
  • Sharmin Sultana
    • 1
  • Frank Verheest
    • 2
    • 3
  1. 1.Centre for Plasma Physics, Department of Physics and AstronomyQueen’s University BelfastBelfastUK
  2. 2.Sterrenkundig ObservatoriumUniversiteit GentGentBelgium
  3. 3.School of PhysicsUniversity of KwaZulu-NatalDurbanSouth Africa