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The Role of a Thick Soliton in the Dynamics of the Soliton Gas Within the Framework of the Gardner Equation

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Radiophysics and Quantum Electronics Aims and scope

We study the statistical moments of the soliton gas (mean field, variance, skewness, and kurtosis), which is described within the framework of the Gardner equation with negative cubic nonlinearity. The influence of the limiting (thick or table-like) soliton on the statistical moments of the soliton gas is considered. It is shown to be substantial if the thick-soliton intensity is comparable with that of the moderate-amplitude solitons.

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References

  1. A. R. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform, Academic Press, Oxford (2010).

    MATH  Google Scholar 

  2. B. G. Konopelchenko, Inv. Probl., 7, 739 (1991).

    Article  ADS  Google Scholar 

  3. G. Fu and H.-E. Tam, J. Math. Anal. Appl., 330, 989 (2007).

    Article  MathSciNet  Google Scholar 

  4. A. M. Wazwaz, Commun. Nonlin. Sci. Numer. Simulat., 12, No. 8, 1395 (2007).

    Article  ADS  Google Scholar 

  5. M. S. Ruderman, T. Talipova, and E. Pelinovsky, J. Plasma Phys., 74, No. 5, 639 (2008).

    Article  ADS  Google Scholar 

  6. S. A. El-Tantawy, E. I. El-Awady, and R. Schlickeiser, Astrophys. Space Sci., 360, 49 (2015).

    Article  ADS  Google Scholar 

  7. S. A. El-Tantawy, Astrophys Space Sci., 361, 164 (2016).

    Article  ADS  Google Scholar 

  8. R. Grimshaw, E. Pelinovsky, T. Talipova, et al., J. Phys. Oceanogr., 34, 2774 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  9. R. Grimshaw, E. Pelinovsky, and T. Talipova, Surv. Geophys., 28, No. 4, 273 (2007).

    Article  ADS  Google Scholar 

  10. R. D. Pingree and G. T. Mardell, Progr. Oceanogr., 14, 413 (1985).

    Article  Google Scholar 

  11. A. L. New and R. D. Pingree, Deep-Sea Res., 39, 1521 (1992).

    Article  ADS  Google Scholar 

  12. T. P. Stanton and L. A. Ostrovsky, Geophys. Res. Lett., 25, No. 14, 2695 (1998).

    Article  ADS  Google Scholar 

  13. E. N. Pelinovsky, E. G. Shurgalina, and A. A. Rodin, Izvestiya, Atmos. Ocean. Phys., 51, No. 5, 530 (2015).

    Article  ADS  Google Scholar 

  14. O. Kurkina, E. Rouvinskaya, T. Talipova, et al., Physica D, 333, 222 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  15. T. Talipova, E. Pelinovsky, O. Kurkina, et al., Shock Vibr., 2015, 875619 (2015).

    Google Scholar 

  16. L. Ostrovsky, E. Pelinovsky, V. Shrira, et al., Chaos, 25, 097620 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  17. D. S. Agafontsev and V. E. Zakharov, Nonlinearity, 29, No. 11, 3551 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  18. A. I. Dyachenko and V. E. Zakharov, JETP Lett., 88, No. 5, 307 (2008).

    Article  ADS  Google Scholar 

  19. N. Akhmediev, J. M. Soto-Crespo, and N. Devine, Phys. Rev. E, 94, 022212 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  20. J. M. Soto-Crespo, N. Devine, and N. Akhmediev, Phys. Rev. Lett., 116, No. 10, 103901 (2016).

    Article  ADS  Google Scholar 

  21. A. R. Osborne, E. Segre, and G. Boffetta, Phys. Rev. Lett., 67, 592 (1991).

    Article  ADS  Google Scholar 

  22. A. R. Osborne, M. Serio, L. Bergamasco, et al., Physica D, 123, 64 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  23. A. Costa, R. O. Alfred, T. R. Donald, et al., Phys. Rev. Lett., 113, 108501 (2014).

    Article  ADS  Google Scholar 

  24. D. Dutykh and E. Pelinovsky, Phys. Lett. A, 378, 3102 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  25. E. N. Pelinovsky, E. G. Shurgalina, A. V. Sergeeva, et al., Phys. Lett. A, 377, Nos. 3–4, 272 (2013).

    Article  ADS  Google Scholar 

  26. G. A. El, Chaos, 26, No. 2, 1 (2016).

    Article  Google Scholar 

  27. D. Dutykh, M. Chhay, and F. Fedele, Comput. Math. Math. Phys., 53, No. 2, 221 (2013).

    Article  MathSciNet  Google Scholar 

  28. E. N. Pelinovsky and E. G. Shurgalina, Radiophys. Quantum Electron., 57, No. 10, 737 (2014).

    Article  ADS  Google Scholar 

  29. E. G. Shurgalina and E. N. Pelinovsky, Dynamics of an Ensemble of Irregular Waves in Near-Shore Area [in Russian], Nizhny Novgorod State Tech. Univ., Nizhny Novgorod (2015).

    Google Scholar 

  30. E. Pelinovsky and E. Shurgalina, “KdV soliton gas: Interactions and turbulence,” in: I. S. Pikovsky, N. F. Rulkov, and L. S. Tsimring, eds., Advances in Dynamics, Patterns, Cognition: Challenges in Complexity, Springer, Cham (2017), p. 295.

    Chapter  Google Scholar 

  31. E. Shurgalina and E. Pelinovsky, Phys. Lett. A, 380, No. 24, 2049 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  32. A. V. Slunyaev and E. N. Pelinovsky, Phys. Rev. Lett., 117, 214501 (2016).

    Article  ADS  Google Scholar 

  33. F. Carbone, D. Dutykh, and G. A. El, Europhys. Lett., 113, No. 3, 30003 (2016).

    Article  Google Scholar 

  34. R. Grimshaw, D. Pelinovsky, E. Pelinovsky, and E. Slunyaev, Chaos, 12, No. 4, 1070 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  35. A. V. Slyunyaev and E. N. Pelinovski, JETP, 89, No. 1, 173 (1999).

    Article  ADS  Google Scholar 

  36. K. A. Gorshkov and I. A. Soustova, Radiophys. Quantum Electron., 44, Nos. 5–6, 465 (2001).

    Article  Google Scholar 

  37. K. A. Gorshkov, I. A. Soustova, A. V. Ermoshkin, and N. V. Zaytseva, Radiophys. Quantum Electron., 55, No. 5, 344 (2012).

    Article  ADS  Google Scholar 

  38. E. N. Pelinovskii and A. V. Slyunyaev, JETP Lett., 67, No. 9, 655 (1998).

    Article  ADS  Google Scholar 

  39. A. V. Slyunyaev, JETP, 92, No. 3, 529 (2001).

    Article  ADS  Google Scholar 

  40. E. G. Shurgalina, Radiophys. Quantum Electron., 60, No. 9, 703 (2017).

    Article  ADS  Google Scholar 

  41. E. G. Shurgalina, Fluid Dyn., 53, No. 1, 59 (2018).

    Article  MathSciNet  Google Scholar 

  42. B. Fronberg, A Practical Guide to Pseudospectral Method, Cambridge Univ. Press, Cambridge (1998).

    Google Scholar 

  43. E. G. Shurgalina, E. N. Pelinovsky, and K. A. Gorshkov, Moscow Univ. Phys. Bull., 72, No. 5, 441 (2017).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    E. G. Didenkulova & E. N. Pelinovsky

  2. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia

    E. G. Didenkulova & E. N. Pelinovsky

Authors
  1. E. G. Didenkulova
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  2. E. N. Pelinovsky
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Correspondence to E. G. Didenkulova.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 8–9, pp. 700–710, August–September 2018.

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Didenkulova, E.G., Pelinovsky, E.N. The Role of a Thick Soliton in the Dynamics of the Soliton Gas Within the Framework of the Gardner Equation. Radiophys Quantum El 61, 623–632 (2019). https://doi.org/10.1007/s11141-019-09922-9

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  • DOI: https://doi.org/10.1007/s11141-019-09922-9

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