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Wave Breaking in Dispersive Fluid Dynamics of the Bose–Einstein Condensate

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Abstract

The problem of wave breaking during its propagation in the Bose–Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form (–x)1/n. The evolution of the wave is described by the Gross–Pitaevskii equation so that a dispersive shock wave is formed as a result of breaking; this wave can be represented using the Gurevich–Pitaevskii approach as a modulated periodic solution to the Gross–Pitaevskii equation, and the evolution of the modulation parameters is described by the Whitham equations obtained by averaging the conservation laws over fast oscillations in the wave. The solution to the Whitham modulation equations is obtained in closed form for n = 2, 3, and the velocities of the dispersion shock wave edges for asymptotically long evolution times are determined for arbitrary integers n > 1. The problem considered here can be applied for describing the generation of dispersion shock waves observed in experiments with the Bose–Einstein condensate.

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Authors and Affiliations

  1. Institute of Spectroscopy, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia

    A. M. Kamchatnov

  2. Moscow Institute of Physics and Technology, 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. M. Kamchatnov

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  1. A. M. Kamchatnov
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Correspondence to A. M. Kamchatnov.

Additional information

Contribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday

Translated by N. Wadhwa

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Kamchatnov, A.M. Wave Breaking in Dispersive Fluid Dynamics of the Bose–Einstein Condensate. J. Exp. Theor. Phys. 127, 903–911 (2018). https://doi.org/10.1134/S1063776118110043

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  • DOI: https://doi.org/10.1134/S1063776118110043

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