Theoretical and Mathematical Physics

, Volume 109, Issue 1, pp 1345–1351 | Cite as

On the asymptotic evolution of a localized perturbation of the one-dimensional Landau-Lifshits equation with uniaxial anisotropy

  • A. M. Kamchatnov
  • A. L. Krylov
  • G. A. El'


The witham method is applied to analyze the modulation instability of plane waves in a one-dimensional ferromagnet described by the Landau-Lifshits equation with uniaxial anisotropy. It is shown that the instability results in the formation of a domain structure in the system.


Anisotropy Plane Wave Domain Structure Modulation Instability Localize Perturbation 
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.
    J. Bernasconi and T. Schneider,Physics in One Dimension, Springer, Berlin (1981).Google Scholar
  2. 2.
    S. E. Trullinger, V. E. Zakharov, and V. L. Pokrovsky,Solitons, North-Holland, Amsterdam (1986).Google Scholar
  3. 3.
    A. R. Bishop, D. K. Campbell, P. Kumar, and S. E. Trullinger,Nonlinearity in Condensed Matter, Springer, Berlin (1987).Google Scholar
  4. 4.
    A. M. Kosevich, B. A. Ivanov, and S. A. Kovalev,Nonlinear Magnetization Waves. Dynamic and Topological Solitons [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
  5. 5.
    V. I. Karpman,Nichtlineare Wellen in Dispersiven Medien [in German], Acad. Verlag, Berlin (1977).Google Scholar
  6. 6.
    G. A. El', A. V. Gurevich, V. V. Khodorovskii, and A. L. Krylov,Phys. Lett. A,177, 357 (1993).Google Scholar
  7. 7.
    G. B. Witham,Linear and Nonlinear Waves, Wiley, New York-London-Sydney-Toronto (1974).Google Scholar
  8. 8.
    A. M. Kamchatnov,Phys. Lett. A,162, 389 (1992).Google Scholar
  9. 9.
    R. F. Bikbaev, A. I. Bobenko, and A. R. Its,Dokl. Akad. Nauk SSSR,272, 1293 (1983).Google Scholar
  10. 10.
    A. I. Bobenko,Funkts. Anal. Prilozhen.,19, 6 (1985).Google Scholar
  11. 11.
    A. M. Kamchatnov,JETP,75, 868 (1992).Google Scholar
  12. 12.
    H. Flaschka, G. Forest, and D. W. McLaughlin,Commun. Pure Appl. Math.,33, 739 (1979).Google Scholar
  13. 13.
    I. M. Krichever,Funkts. Anal. Prilozhen.,22, No. 3, 37 (1988).Google Scholar
  14. 14.
    A. M. Kamchatnov,Phys. Lett. A,186, 389 (1994).Google Scholar
  15. 15.
    A. M. Kamchatnov,JETP,70, 80 (1990).Google Scholar
  16. 16.
    A. V. Gurevich, A. L. Krylov, and G. A. El',JETP Lett.,54, 102 (1991).Google Scholar
  17. 17.
    V. R. Kudashev,JETP Lett.,54, 175 (1991).Google Scholar
  18. 18.
    M. V. Pavlov,Theor. Math. Phys.,71, 584 (1987).Google Scholar
  19. 19.
    A. V. Gurevich and L. P. Pitaevskii,JETP,38, 291 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • A. M. Kamchatnov
    • 1
  • A. L. Krylov
    • 2
  • G. A. El'
    • 3
  1. 1.Troitsk Institute of Innovative and Thermonuclear StudiesTroitsk, Moscow RegionRussia
  2. 2.O. Yu. Schmidt Institute of Earth PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Institute for Terrestrial Magnetism, Ionosphere, and Radio Wave PropagationRussian Academy of SciencesTroitsk, Moscow RegionRussia

Personalised recommendations