Skip to main content
SpringerLink
Log in

Adiabatic elimination based on functional differentiation in the nonlinear and spatially distributed cases

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

A method of adiabatic elimination is proposed based on the use of the Furutsu-Novikov formula. A case of two nonlinear Langevin equations and a spatially distributed problem typical for the nonlinear wave propagation in random media have been considered. The method not only permits adiabatic elimination of the fast-decaying variable from the equation for the slow-decaying one but also allows for the return effect of the slow-decaying subsystem on the fast-decaying one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gardiner, C.W.: Handbook of stochastic methods. Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  2. Grabert, H., Talkner, P., Hänggi, P.: Z. Phys. B — Condensed Matter and Quanta26, 389 (1977)

    Google Scholar 

  3. Haake, F.: Z. Phys. B — Condensed Matter48, 31 (1982)

    Google Scholar 

  4. Chaturvedi, S.: Z. Phys. B — Condensed Matter51, 271 (1983)

    Google Scholar 

  5. Tokuyama, M., Mori, H.: Prog. Theor. Phys.55, 411 (1976)

    Google Scholar 

  6. Van Kampen, N.G.: Physica A74, 215 239 (1974)

    Google Scholar 

  7. Terwel, R.H.: Physica A74, 248 (1974)

    Google Scholar 

  8. Haken, H.: Advanced synergetics, Instability hierarchies of self-organizing systems and devices. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  9. Kaneko, K.: Prog. Theor. Phys.66, 129 (1981)

    Google Scholar 

  10. Hänggi, P.: Z. Phys. B — Condensed Matter and Quanta31, 407 (1978)

    Google Scholar 

  11. Fox, R.F.: Phys. Rev. A33, 467 (1986)

    Google Scholar 

  12. Gardiner, C.W., Stein-Ross, M.L.: Phys. Rev. A29, 2823 (1984)

    Google Scholar 

  13. Stein-Ross, M.L., Gardiner, C.W.: Phys. Rev. A29, 2834 (1984)

    Google Scholar 

  14. Hänggi, P., Marchesoni, F., Grigolini, P.: Z. Phys. B — Condensed Matter56, 333 (1984)

    Google Scholar 

  15. Leiter, T., Marchesoni, F., Risken, H.: Phys. Rev. A38, 983 (1988)

    Google Scholar 

  16. Hänggi, P., Mroczkowski, Th., Moss, F., McClintock, P.V.E.: Phys. Rev. A32, 695 (1985)

    Google Scholar 

  17. Klyatzkin, V.I.: Statistical description of dynamical systems with fluctuating parameters. Moskow: Nauka 1977

    Google Scholar 

  18. Fedoriuk, M.V.: Steepest descent method. Moskow: Nauka 1977

    Google Scholar 

  19. Raymer, M., Mostowski, J.: Phys. Rev. A24, 1980 (1981)

    Google Scholar 

  20. Hopf, E.: Rat. Mech. Anal.1, 87 (1952)

    Google Scholar 

  21. Malakhov, A.N., Saichev, A.I.: J. Exp. Theor. Phys. (Soviet)17, 699 (1974)

    Google Scholar 

  22. Shapiro, V.E., Loginov, B.M.: Dynamical systems under random perturbations. Simple means of analysis. Moscow: Nauka 1983

    Google Scholar 

  23. Pitovanov, S.E., Chetverikov, V.M.: Theor. Math. Phys. (Soviet)35, 211 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics BSSR Academy of Sciences, Leninsky prosp. 70, SU-220602, Minsk, USSR

    I. I. Fedchenia

Authors
  1. I. I. Fedchenia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedchenia, I.I. Adiabatic elimination based on functional differentiation in the nonlinear and spatially distributed cases. Z. Physik B - Condensed Matter 82, 441–451 (1991). https://doi.org/10.1007/BF01357193

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01357193

Keywords

Search

Navigation