Communications in Mathematical Physics

, Volume 195, Issue 2, pp 267–293

Unstable BGK Solitary Waves and Collisionless Shocks

  • Yan Guo
  • Walter A. Strauss

DOI: 10.1007/s002200050389

Cite this article as:
Guo, Y. & Strauss, W. Comm Math Phys (1998) 195: 267. doi:10.1007/s002200050389


Consider a collisionless relativistic neutral plasma. We generalize the Penrose condition for linearized instability to the relativistic case. Then we consider a general one-dimensional equilibrium (a BGK wave) that is a collisionless shock or a solitary wave. The electric potential undergoes a transition from one constant to another as $x$ runs from −∞ to +∞. We prove that if one of these constants satisfies the relativistic version of the Penrose condition, then the BGK wave is nonlinearly unstable. We also prove that the periodic relativistic BGK waves of small amplitude are nonlinearly unstable.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Yan Guo
    • 1
  • Walter A. Strauss
    • 2
  1. 1.Division of Applied Mathematics, Brown University, Providence, RI 02912, USAUS
  2. 2.Department of Mathematics, Brown University, Providence, RI 02912, USAUS