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Number of Solitons Generated from an Intense Initial Pulse at Asymptotically Large Time

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Abstract

A method to derive formulas for the number of solitons into which a sufficiently intense initial pulse in the form of a localized simple wave evolves at asymptotically large time has been proposed on the basis of the Gurevich–Pitaevskii theorem on the number of oscillations entering the dispersive shock wave region. In application to integrable equations, this method reproduces Karpman-type formulas following from the semiclassical approximation for a linear spectral problem associated with the considered equation. It has been shown on particular examples that expressions previously obtained by means of the formal continuation of the solution of modulation Whitham equations to the dispersionless region of the wave can be derived in the case of nonintegrable equations.

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ACKNOWLEDGMENTS

I am grateful to L.P. Pitaevskii and G.A. El for stimulating discussions.

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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 (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. M. Kamchatnov

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Correspondence to A. M. Kamchatnov.

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Translated by R. Tyapaev

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Kamchatnov, A.M. Number of Solitons Generated from an Intense Initial Pulse at Asymptotically Large Time. J. Exp. Theor. Phys. 132, 63–72 (2021). https://doi.org/10.1134/S106377612101012X

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  • DOI: https://doi.org/10.1134/S106377612101012X

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