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KDV Soliton Gas: Interactions and Turbulence

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Advances in Dynamics, Patterns, Cognition

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 20))

Abstract

The collective behavior of soliton ensemble corresponded to soliton turbulence is studied within the integrable Korteweg–de Vries (KdV) equation. Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. The amplitude of the resulted impulse decreases during the nonlinear interaction. It leads to the changing of characteristics of whole multi-soliton field. Numerical simulation of soliton ensemble within the KdV equation is performed. Statistical moments of wave fields and distribution functions of wave amplitudes are found and analyzed. Skewness and kurtosis decrease due to soliton interaction. The criterion of “small” soliton’s negative velocity in soliton gas is obtained.

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Acknowledgements

Different parts of the study were funded by RFBR (16-02-00167, 16-05-00049, 16-35-00175). The study of the effect of a negative soliton velocity was particularly funded by RFBR (16-32-60012). The authors also gratefully acknowledge the support from Volkswagen Foundation and President grant SC-6637.2016.5.

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Authors and Affiliations

  1. Institute of Applied Physics, Nizhny Novgorod, Russia

    Efim Pelinovsky & Ekaterina Shurgalina

  2. Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

    Efim Pelinovsky

  3. National Research University – Higher School of Economics, Nizhny Novgorod, Russia

    Efim Pelinovsky

Authors
  1. Efim Pelinovsky
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  2. Ekaterina Shurgalina
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Correspondence to Efim Pelinovsky .

Editor information

Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    Igor S. Aranson

  2. Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  3. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Nikolai F. Rulkov

  4. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Lev S. Tsimring

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Pelinovsky, E., Shurgalina, E. (2017). KDV Soliton Gas: Interactions and Turbulence. In: Aranson, I., Pikovsky, A., Rulkov, N., Tsimring, L. (eds) Advances in Dynamics, Patterns, Cognition. Nonlinear Systems and Complexity, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-53673-6_18

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  • DOI: https://doi.org/10.1007/978-3-319-53673-6_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53672-9

  • Online ISBN: 978-3-319-53673-6

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