Solitons in Disordered Systems or Application of Catastrophe Theory to Solitons

  • F. V. Kusmartsev
Part of the Recent Progress in Many-Body Theories book series (RPMT, volume 1)


The problem of the soliton existence in a disordered system is connected with the question of the soliton existence in a homogeneous medium [1]. Generally speaking the answer to the question of the existence and stability of solition can be found by means of the mathematical theory of the singularity function, which is usually called as the catastrophe theory [2]. From the point of view of this theory we construct some functional in the functional space of the wave function. From this functional we can obtain the equation, which defines the soliton solution. On the other hand our functional defines some surface S. The extrema of this surface correspond to soliton solution. If we take the minima of this surface then the soliton, corresponding to this stationary point, is a stable one. The other extrema S (different of minima) correspond to an unstable soliton. Let us consider simple examples.


Soliton Solution Langmuir Wave Catastrophe Theory Virial Theorem Landau Institute 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1].
    F.V. Kusmartsev, Physica Scripta 29:7 (1984)CrossRefGoogle Scholar
  2. [2].
    Tim Poston, Ian Stewart, Catastrophe theory and its applications. Pitman London (1978).Google Scholar
  3. [3].
    J. Juul Rasmussen, K. Rypdal, Physica Scripta, 33:481 (1986)CrossRefGoogle Scholar
  4. [4].
    V.E. Zakharov, A.F. Maistrukov, V.S. Sinah, Fiz. plasma, 1:614 (1975)Google Scholar
  5. [5].
    F.V. Kusmartsev, E.I. Rashba, Zh. Eksp. Teor. Fiz., 84:2064 (1983); Sov. Phys–JETP 57(6):1202 (1983)Google Scholar
  6. [6].
    V.E. Zakharov, Zh. Eksp. Teor. Fiz. 62: 1745 (1972)Google Scholar
  7. [7].
    P.K. Kaw, K. Nishikawa, Y. Yosliida and A. Hasegawa, Phys. Rev. Lett., 35:88 (1975)CrossRefGoogle Scholar
  8. [8].
    E.M. Laedke, K.H. Spatschek, Phys. Rev. Lett. 52:279 (1984)CrossRefGoogle Scholar
  9. [9].
    F.V. Kusmartsev, Plasma Physics and Contr. Fus. 29:437 (1987)Google Scholar
  10. [10].
    A.Y. Wong, P.Y. Cheung, Phys. Rev. Lett. 52:1222 (1984)CrossRefGoogle Scholar
  11. [11].
    D.T. Escande, B. Soillard, Phys. Rev. Lett. 52:1296 (1984)CrossRefGoogle Scholar
  12. [12].
    F.V. Kusmartsev, “Soliton in random media”, Preprint of Landau Institute 1985–19: (1985); Fiz. Tverd. Tel. 28:892 (1986); Phys. Lett. A121:71 (1987)Google Scholar
  13. [13].
    F.V. Kusmartsev, E.I. Rashba, Fiz. Tekh. Polupr., 18:691 (1984).Google Scholar
  14. [14].
    G.H. Derrick, J. Math. Phys., 5:1252 (1964).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • F. V. Kusmartsev
    • 1
  1. 1.L.D. Landau Institute for Theoretical PhysicsMoscowUSSR

Personalised recommendations