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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 Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för maskinteknik.
2017 (Engelska)Ingår i: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 96, nr 1, s. 399-402Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
MAIK NAUKA/INTERPERIODICA/SPRINGER , 2017. Vol. 96, nr 1, s. 399-402
Nyckelord [en]
BURGERS-EQUATION; DYNAMICS
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:bth-15160DOI: 10.1134/S1064562417040238ISI: 000409365100025OAI: oai:DiVA.org:bth-15160DiVA, id: diva2:1143235
Tillgänglig från: 2017-09-21 Skapad: 2017-09-21 Senast uppdaterad: 2017-09-29Bibliografiskt granskad

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Rudenko, Oleg

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