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One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2017 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 96, no 1, 399-402 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER , 2017. Vol. 96, no 1, 399-402 p.
Keyword [en]
BURGERS-EQUATION; DYNAMICS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-15160DOI: 10.1134/S1064562417040238ISI: 000409365100025OAI: oai:DiVA.org:bth-15160DiVA: diva2:1143235
Available from: 2017-09-21 Created: 2017-09-21 Last updated: 2017-09-29Bibliographically approved

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Rudenko, Oleg
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