Advertisement

Theoretical and Mathematical Physics

, Volume 91, Issue 1, pp 418–427 | Cite as

A class of exact solutions for a kinetic model of an equilibrium plasma

  • Yu. A. Markov
Article

Abstract

The stationary Vlasov-Maxwell system is reduced to a “resolving” equation of sinh-Gordon type. It is shown that for fully ionized hydrogen and helium plasmas the resolving equation will have the form of the sinh-Gordon equation and Bullough-Dodd-Zhiber-Shabat equation (with elliptic operator), respectively. Hirota's method is used to obtain exact solutions for these equations. From these solutions, the characteristics of the system are recovered: the distribution functions and the self-consistent electromagnetic field.

Keywords

Hydrogen Distribution Function Helium Exact Solution Kinetic Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. B. Movsesyants,Zh. Eksp. Teor. Fiz.,91, 493 (1986).Google Scholar
  2. 2.
    A. V. Samokhin,Dokl. Akad. Nauk SSSR,285, 1101 (1985).Google Scholar
  3. 3.
    G. A. Rudykh, N. A. Sidorov, and A. V. Sinitsyn,Dokl. Akad. Nauk SSSR,302, 594 (1988).Google Scholar
  4. 4.
    Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, and A. V. Sinitsyn,Mat. Mod.,1, 95 (1989).Google Scholar
  5. 5.
    R. K. Dodd and R. K. Bullough,Proc. R. Soc. London, Ser. A,352, 481 (1977).Google Scholar
  6. 6.
    A. V. Zhiber and A. B. Shabat,Dokl. Akad. Nauk SSSR,247, 1103 (1979).Google Scholar
  7. 7.
    R. K. Bullough and P. J. Caudrey (eds.),Solitons, Springer, Berlin (1980).Google Scholar
  8. 8.
    A. N. Leznov and M. V. Savel'ev,Group Methods of Integrating Nonlinear Dynamical Systems [in Russian], Nauka, Moscow (1985).Google Scholar
  9. 9.
    R. C. Davidson,Theory of Non-Neutral Plasmas (Frontiers in Physics, Vol. 43), Reading, Mass. (1974).Google Scholar
  10. 10.
    V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii,The Theory of Solitons [in Russian], Nauka, Moscow (1980).Google Scholar
  11. 11.
    Yu. A. Markov,Dokl. Akad. Nauk SSSR,308, 80 (1989).Google Scholar
  12. 12.
    G. L. Lamb,Elements of Soliton Theory, Wiley-Interscience (1980).Google Scholar
  13. 13.
    A. B. Borisov and V. V. Kiselyev,Physica (Utrecht) D,31, 49 (1988).Google Scholar
  14. 14.
    J. M. Finn and P. K. Kaw,Phys. Fluids,20, 72 (1977).Google Scholar
  15. 15.
    V. M. Fadeev, I. F. Kvartskhava, and N. N. Komarov,Yad. Sintez.,5, 202 (1965).Google Scholar
  16. 16.
    R. Hirota,J. Phys. Soc. Jpn. 33, 1459 (1972).Google Scholar
  17. 17.
    M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths., Vol. 4), Philadelphia (1981).Google Scholar
  18. 18.
    A. B. Borisov, G. G. Talits, A. P. Tankeev, and G. V. Bezmaternykh, “Vortices and solitons of the two-dimensional sin-Gordon equation,” in:Modern Problems of the Theory of Magnetism [in Russian], Naukova Dumka, Kiev (1986), pp. 103–111.Google Scholar
  19. 19.
    E. M. Lifshitz and L. P. Pitaevskii,Theoretical Physics, Vol. 10.Physical Kinetics [in Russian], Nauka, Moscow (1979).Google Scholar
  20. 20.
    O. V. Kaptsov,Dokl. Akad. Nauk SSSR,298, 597 (1988).Google Scholar
  21. 21.
    A. V. Mikhailov,Pis'ma Zh. Eksp. Teor. Fiz.,30, 443 (1979).Google Scholar
  22. 22.
    A. C. Ting, H. H. Chen, and Y. C. Lee,Physica (Utrecht) D,26, 37 (1987).Google Scholar
  23. 23.
    M. V. Babich,Algebra Analiz.,2, 63 (1990).Google Scholar
  24. 24.
    I. Yu. Cherdantsev and R. A. Sharipov,Teor. Mat. Fiz.,82, 155 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Yu. A. Markov

There are no affiliations available

Personalised recommendations