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Issue 10, 2026
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Physics of our days


Gurevich—Pitaevskii problem and its development

 a, b
a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russian Federation
b Institute of Spectroscopy, Russian Academy of Sciences, ul. Fizicheskaya 5, Troitsk, Moscow, 108840, Russian Federation

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.

Fulltext pdf (1003 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2020.08.038815
Keywords: soliton, dispersive shock wave, Bose—Einstein condensate, nonlinear optics, Gurevich—Pitaevskii problem, Whitham method
PACS: 03.75.Kk, 03.75.Lm, 05.45.Yv, 42.65.−k, 42.65.Tg, 47.35.Fg, 67.85.Fg (all)
DOI: 10.3367/UFNe.2020.08.038815
URL: https://ufn.ru/en/articles/2021/1/d/
000632470400003
2-s2.0-85095480354
2021PhyU...64...48K
Citation: Kamchatnov A M "Gurevich—Pitaevskii problem and its development" Phys. Usp. 64 48–82 (2021)
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Received: 21st, July 2020, 11th, August 2020

Оригинал: Камчатнов А М «Задача Гуревича—Питаевского и её развитие» УФН 191 52–87 (2021); DOI: 10.3367/UFNr.2020.08.038815

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