Skip to main content
SpringerLink
Log in

Three-wave interaction including frequency doubling effects

  • Published:
Soviet Physics Journal Aims and scope

Abstract

A technique is developed in this work to construct asymptotic solutions describing the resonant interaction of shortwaves in weakly nonlinear dispersive media. Also included is the process of generation of multiple harmonics for low dispersion. A calculation of the acoustooptical interaction is performed, including the generation of multiple harmonics of acoustic waves.

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

Literature cited

  1. E. B. Gledzer, F. V. Dolzhanskii, and A. M. Obykhov, Systems of the Hydrodynamic Type and Their Applications [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. O. M. Phillips, The Dynamics of the Upper Ocean, Cambridge Univ. Press, Cambridge (1966).

    Google Scholar 

  3. S. A. Akhmanov and K. V. Khokhlov, Problems in Nonlinear Optics; Electromagnetic Waves in Nonlinear Dispersive Media, Gordon & Breach, New York (1972).

    Google Scholar 

  4. N. Bloembergen, Nonlinear Optics, W. A. Benjamin, New York (1965).

    Google Scholar 

  5. B. B. Kadomtsev, Collective Phenomena in a Plasma [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  6. K. Hasselman, J. Fluid Mech.,12, 481 (1962).

    Google Scholar 

  7. J. Weiland and H. Wilhelmsson, Coherent Nonlinear Interaction of Waves in a Plasma, Oxford, New York (1977).

    Google Scholar 

  8. A. Yariv, Introduction to Optical Electronics, Holt, Rinehart & Winston, New York (1976).

    Google Scholar 

  9. V. E. Zakharov, in: Solitons [Russian translation], Mir, Moscow (1983), pp. 270–309.

    Google Scholar 

  10. V. P. Maslov, Usp. Mat. Nauk,38, No. 6, 3 (1983).

    Google Scholar 

  11. V. P. Maslov, Mathematical Aspects of Integral Optics [in Russian], MIEM, Moscow (1983).

    Google Scholar 

  12. V. P. Maslov, Resonance Processes in Wave Theory and Self-Focusing [in Russian], MIEM, Moscow (1983).

    Google Scholar 

  13. L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media, Pergamon, New York (1960).

    Google Scholar 

  14. V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Moscow State University, Moscow (1965).

    Google Scholar 

  15. V. P. Maslov and M. V. Fedoryuk, Semi-Classical Approximation in Quantum Mechanics, Reidel, Boston (1981).

    Google Scholar 

  16. V. I. Arnol'd, Usp. Mat. Nauk,18, No. 6, 21 (1963).

    Google Scholar 

  17. J. Moser, Lectures on Hamiltonian Systems [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  18. L. K. Zarembo and V. N. Timoshenko, Nonlinear Acoustics [in Russian], Moscow State University, Moscow (1984).

    Google Scholar 

  19. J. Ziman, Electrons and Phonons, Clarendon Press, Oxford (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Electronic Machine Design, USSR

    V. P. Maslov & G. A. Omel'yanov

Authors
  1. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. A. Omel'yanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–23, March, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P., Omel'yanov, G.A. Three-wave interaction including frequency doubling effects. Soviet Physics Journal 29, 157–175 (1986). https://doi.org/10.1007/BF00891878

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00891878

Keywords

Search

Navigation