Instability of periodic BGK waves

Mathematical Research Letters

Volumn 8, Issue 4, 2001, Pages 521-534

  Lin, Zhiwu ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035539221     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2001.v8.n4.a11     Document Type: Article

References (18)

1. [1] Bernstein, I., Greene, J., Kruskal, M., Exact nonlinear plasma oscillations. Phys. Rev. 108, 3, 546-550 (1957).
2. [2] Armstrong, T., Montgomery, D., Asymptotic state of the two-stream instability, J.Plasma. Physics, 1, part 4, 425-433 (1967).
3. [3] Goldman, M. V., Theory of stability of large periodic plasma waves, Phys. Fluids, 13, no. 3, 1281-1289 (1970).
4. [4] Schwarzmeier, J. L., Lewis, H. R., Abraham-Schrauner, B., Symon, K. R., Stability of Bernstein-Greene-Kruskal equilibria, Phys. Fluids, 22, no. 9, 1747-1760 (1979).
5. [5] Gizzo, A., Izrar, B., Bertrand, P., Fijalkow, E., Feix, M. R., Shoucri, M., Stability of Bernstein-Greene-Kruskal plasma equilibria. Numerical experiments over a long time, Phys. Fluids, 31, no. 1, 72-82 (1988).
6. [6] Manfredi, G., Bertrand, P., Stability of Bernstein-Greene-Kruskal modes, Phys. Plasmas, 7, 6, 2425-2431 (2000).
7. [7] Grillakis, M., Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Comm. Pure Appl. Math. 41, no. 6, 747-774 (1988).
8. [8] Guo, Y., Stable magnetic equilibria in collisionless plasma, Comm. Pure Appl. Math., Vol L, 0891-0933 (1997).
9. [9] Guo, Y., Stable magnetic equilibria in a symmetric plasma, Commun. Math. Phys., 200, 211-247 (1999).
10. [10] Guo, Y., Strauss, W., Instability of periodic BGK equilibria, Comm. Pure Appl. Math. Vol XLVIII, 861-894 (1995).
11. [11] Guo, Y., Strauss, W., Unstable relativistic BGK waves, Comp. and Appl. Math., 18, no. 1, 87-122 (1999).
12. [12] Guo, Y., Strauss, W., Unstable BGK solitary waves and collisionless shocks, Commun. Math. Phys. 195, 249-265 (1998).
13. [13] Guo, Y., Strauss, W., Unstable oscillatory-tail solutions, SIAM J. Math. Anal., 30, no. 5, 1076-1114 (1999).
14. [14] Guo, Y., Strauss, W., Magnetically created instability in a collisionless plasma, J. Math. Pures. Appl., 79, no. 10, 975-1009 (2000).
15. [15] Golse, F., Lions, P. L., Perthame, B., and Sentis, R., Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 76, no. 1, 110-125 (1988).
16. [16] DiPerna, R. J., Lions, P. L., Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., Vol XLII, 729-757 (1989).
17. [17] Reed, M., Simon, B., Methods of modern mathematical physics, Vol IV, Academic press 1978.
18. [18] Kato, T., Perturbation theory for linear operators, Springer 1976.