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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 3, Pages 415–424
DOI: https://doi.org/10.4213/tmf9800 (Mi tmf9800) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Motion of dispersive shock edges in nonlinear pulse evolution

A. M. Kamchatnov

Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, Russia
Full-text PDF (382 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9800
Abstract: We formulate a method for calculating the velocities of the edges of dispersive shock waves that are generated after wave breaking of pulses during their propagation in a nonlinear medium. The method is based on the properties of the Whitham modulation system at its degenerate limits obtained for either a vanishing amplitude of oscillations at one edge or a vanishing wave number at the other edge.
Keywords: nonlinear wave, soliton, dispersive shock wave, Whitham theory.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00063
This research was supported by the Russian Foundation for Basic Research (Grant No. 20-01-00063).
Received: 28.08.2019
Revised: 28.08.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 3, Pages 363–370
DOI: https://doi.org/10.1134/S0040577920030083
Bibliographic databases:
Document Type: Article
PACS: 01.30.Cc, 03.75.Lm, 05.45.Yv
MSC: 35B40, 35C20, 35Q51,35Q55
Language: Russian
Citation: A. M. Kamchatnov, “Motion of dispersive shock edges in nonlinear pulse evolution”, TMF, 202:3 (2020), 415–424; Theoret. and Math. Phys., 202:3 (2020), 363–370
Citation in format AMSBIB
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\paper Motion of dispersive shock edges in nonlinear pulse evolution
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Linking options:
  • https://www.mathnet.ru/eng/tmf9800
  • https://doi.org/10.4213/tmf9800
  • https://www.mathnet.ru/eng/tmf/v202/i3/p415
    • This publication is cited in the following 3 articles:
    1. A. M. Kamchatnov, “Gurevich–Pitaevskii problem and its development”, Phys. Usp., 64:1 (2021), 48–82  mathnet  crossref  crossref  adsnasa  isi  elib
    2. A. M. Kamchatnov, “Number of solitons generated from an intense initial pulse at asymptotically large time”, J. Exp. Theor. Phys., 132:1 (2021), 63–72  crossref  isi
    3. Kamchatnov A.M., “Theory of Quasi-Simple Dispersive Shock Waves and Number of Solitons Evolved From a Nonlinear Pulse<?a3B2 Show [Editpick]?>”, Chaos, 30:12 (2020), 123148  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:316
    Full-text PDF :81
    References:49
    First page:11
     
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