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One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media

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Abstract

Solutions of the equation describing the high-intensity wave profile within the focal region are derived. This equation is similar to the previously studied models with quadratic and modular nonlinearities, but it is adapted for cubic and quadratically-cubic (QC) nonlinear media, where other physical processes are realized. This simplified one-dimensional equation can be regarded as a “projection” of a three-dimensional equation of Khokhlov–Zabolotskaya type (KZ) onto the axis of the wave beam. Stationary profiles at high intensities of focused waves turn out to be periodic sequences of half-periods of triangular shape with singularities of the derivative at extremum points. Such profiles are typical for nonlinear systems with low-frequency dispersion. There is shown to exist a saturation effect–the amplitude of the wave in the focus cannot exceed a certain maximum value, which does not depend on the initial amplitude.

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Authors and Affiliations

  1. Physics Faculty, Moscow State University, Moscow, 119991, Russia

    O. V. Rudenko

  2. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

    O. V. Rudenko

  3. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

    O. V. Rudenko

  4. Blekinge Institute of Technology, Karlskrona, Sweden

    O. V. Rudenko

Authors
  1. O. V. Rudenko
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Correspondence to O. V. Rudenko.

Additional information

Published in Russian in Doklady Akademii Nauk, 2017, Vol. 475, No. 5, pp. 503–507.

The article was translated by the author.

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Rudenko, O.V. One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media. Dokl. Math. 96, 399–402 (2017). https://doi.org/10.1134/S1064562417040238

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  • DOI: https://doi.org/10.1134/S1064562417040238

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