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Uspekhi Fizicheskikh Nauk, 2021, Volume 191, Number 1, Pages 52–87
DOI: https://doi.org/10.3367/UFNr.2020.08.038815 (Mi ufn6883) 		 
This article is cited in 21 scientific papers (total in 22 papers)

PHYSICS OF OUR DAYS

Gurevich–Pitaevskii problem and its development

A. M. Kamchatnovab

a Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
Full-text PDF (1167 kB) Citations (22)
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DOI: https://doi.org/10.3367/UFNr.2020.08.038815
Abstract: We present an introduction to the theory of dispersive shock waves in the framework of the approach proposed by Gurevich and Pitaevskii (Zh. Eksp. Teor. Fiz., Vol. 65, p. 590 (1973) [Sov. Phys. JETP, Vol. 38, p. 291 (1974)]) based on Whitham's theory of modulation of nonlinear waves. We explain how Whitham equations for a periodic solution can be derived for the Korteweg–de Vries equation and outline some elementary methods to solve them. We illustrate this approach with solutions to the main problems discussed by Gurevich and Pitaevskii. We consider a generalization of the theory to systems with weak dissipation and discuss the theory of dispersive shock waves for the Gross–Pitaevskii equation.
Received: July 21, 2020
Accepted: August 11, 2020
English version:
Physics–Uspekhi, 2021, Volume 64, Issue 1, Pages 48–82
DOI: https://doi.org/10.3367/UFNe.2020.08.038815
Bibliographic databases:
Document Type: Article
PACS: 03.75.Kk, 03.75.Lm, 05.45.Yv, 42.65.-k, 42.65.Tg, 47.35.Fg, 67.85.Fg
Language: Russian
Citation: A. M. Kamchatnov, “Gurevich–Pitaevskii problem and its development”, UFN, 191:1 (2021), 52–87; Phys. Usp., 64:1 (2021), 48–82
Citation in format AMSBIB
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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