Distribution functions of gas of solitons of Korteweg – de Vries-type equation

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

The statistical properties of a rarefied soliton gas are studied using solitary waves – solutions of the generalized Korteweg – de Vries equation as an example. It is shown that there is a critical density of a soliton gas regardless of the type of nonlinearity in the generalized Korteweg – de Vries equation, which is associated with the repulsion of solitons of the same polarity. The first two statistical moments of the wave field (the mean value and the dispersion), which are simultaneously invariants of the Korteweg – de Vries-type equation, are calculated. The densities of the distribution function of a rarefied soliton gas are calculated. A feature in these functions in the region of small field values due to the overlap of the exponential tails of the solitons is noted.

全文:

受限制的访问

作者简介

E. Pelinovsky

Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences; National Research University – Higher School of Economics

编辑信件的主要联系方式.
Email: pelinovsky@ipfran.ru
俄罗斯联邦, Nizhny Novgorod; Nizhny Novgorod

S. Gurbatov

National Research Nizhny Novgorod State University named after N.I. Lobachevsky

Email: gurb@rf.unn.ru
俄罗斯联邦, Nizhny Novgorod

参考

  1. Захаров В.Е. Кинетическое уравнение для солитонов // ЖЭТФ. 1971. Т. 60. С. 993–1000.
  2. El G.A. Soliton gas in integrable dispersive hydrodynamics // J. Stat. Mech. 2021. V. 11. 114001.https://doi.org/10.1088/1742-5468/ac0f6d
  3. Bonnemain T., Doyon B., El G. Generalized hydrodynamics of the KdV soliton gas // J. Phys. A: Math. Theor. 2022. V. 55. 374004. https://doi.org/10.1088/1751-8121/ac8253
  4. Congy T., El G., Tovbis R.A. Dispersive hydrodynamics of soliton condensates for the Korteweg–de Vries Equation // J. Nonlinear Sci. 2023. V. 33. 104. https://doi.org/10.1007/s00332-023-09940-y
  5. Suret P., Randoux S., Gelash A., Agafontsev D., Doyon B., El G. Soliton gas: theory, numerics and experiments // Physical Review E. 2024, V. 109. № 6. 061001. https://doi.org/10.1103/PhysRevE.109.061001
  6. Redor I. Barthelemy E., Michallet H., Onorato M., Mordant N. Experimental evidence of a hydrodynamic soliton gas // Physical Review Letters. 2019, V. 122. № 21. 214502. https://doi.org/10.1103/PhysRevLett.122.214502
  7. Fache L., Damart H., Copie F., Bonnemain T., Congy T., Roberti G., Suret P., El G., Randoux S. Dissipation-driven emergence of a soliton condensate in a nonlinear electrical transmission line // arXiv:2407.02874v1 [nlin.PS]. 2024. https://doi.org/10.48550/arXiv.2407.02874
  8. Costa A., Osborne A.R., Resio D.T., Alessio S., Chiriv E., Saggese E., Bellomo K.., Long C. E. Soliton turbulence in shallow water ocean surface waves // Phys. Rev. Lett. 2014. V. 113. 108501. https://doi.org/10.1103/PhysRevLett.113.108501
  9. Osborne A.R., Resio D.T., Costa A., de Leon S.P., Chiriv E. Highly nonlinear wind waves in Currituck Sound: dense breather turbulence in random ocean waves // Ocean Dynamics. 2019. V. 31. P. 187–219. https://doi.org/10.1007/s10236-018-1232-y
  10. Shurgalina E.G., Pelinovsky E.N. Nonlinear dynamics of a soliton gas: modified Korteweg-de Vries equation framework // Physics Letters A. 2016, V. 380. P. 2049–2053. https://doi.org/10.1016/j.physleta.2016.04.023
  11. Gelash A., Agafontsev D.S. Strongly interacting soliton gas and formation of rogue waves // Phys. Rev. E. 2018. V. 98. 042210. https://doi.org/10.1103/PhysRevE.98.042210
  12. Dutykh D., Pelinovsky E. Numerical simulation of a solitonic gas in KdV and KdV-BBM equations // Physics Letters A 2014, V. 378, P. 3102–3110. https://doi.org/10.1016/j.physleta.2014.09.008
  13. Flamarion M.V., Pelinovsky E.N., Didenkulova E. Non-integrable soliton gas: the Schamel equation framework // Chaos, Solitons & Fractals. 2024. V. 180. 114495. https://doi.org/10.1016/j.chaos.2024.114495
  14. Schamel H., Chakrabarti N. On the evolution equations of nonlinearly permissible, coherent hole structures propagating persistently in collisionless plasmas // Ann. Phys. 2023. V. 535. 2300102. https://doi.org/10.1002/andp.202300102
  15. Могилевич Л.И., Блинков Ю. А., Попова Е.В., Попов В.С. Уединенные волны деформации в двух коаксиальных оболочках из материала с комбинированной нелинейностью, образующих стенки каналов кольцевого и круглого сечения, заполненных вязкой жидкостью // Известия вузов. Прикладная нелинейная динамика. 2024. Т. 32. № 4. С. 521–540. https://doi.org/10.18500/0869-6632-003115
  16. Гурбатов С.Н., Малахов А.Н., Саичев А.И. Нелинейные случайные волны в средах без дисперсии. М.: Наука, 1990. 216 c.
  17. Гурбатов С.Н., Руденко О.В., Саичев А.И. Волны и структуры в нелинейных средах без дисперсии. Приложения к нелинейной акустике. М.: Физматлит, 2008. 496 с.
  18. Шургалина Е.Г., Пелиновский Е.Н. Динамика ансамбля нерегулярных волн в прибрежной зоне. Нижний Новгород: НГТУ, 2015. 179 с.
  19. El G.A. Critical density of a soliton gas // Chaos. 2016. V. 26. 023105. https://doi.org/10.1063/1.4941372
  20. Руденко О.В., Чиркин А.С. О статистике шумовых разрывных волнах в нелинейных средах // ДАН СССР. 1975. Т. 225. № 3. С. 520–523.
  21. Руденко О.В. Взаимодействие интенсивных шумовых волн // Успехи физ наук. 1986. Т. 149. № 3. С. 413–447. https://doi.org/10.3367/UFNr.0149.198607c.0413
  22. Гурбатов С.Н., Пелиновский Е.Н. О вероятностных распределениях римановой волны и интеграла от нее // Доклады РАН. Физика, технические науки. 2020. T. 493. № 1. С. 18–22. https://doi.org/10.31857/S2686740020040070

补充文件

附件文件
动作
1. JATS XML
下载
2. Fig. 1. One of the realizations of the Shamelev soliton gas [13].

下载 (153KB)
索引源数据
3. Fig. 2. Distributions (14) for the Korteweg – de Vries equation (α = 2, 1), the modified Korteweg – de Vries equation (α = 3, 2) and the Schamel equation (α = 3/2, 3).

下载 (63KB)
索引源数据
4. Fig. 3. Distribution density of soliton gas within the framework of the Korteweg – de Vries equation (α = 2, 1), the modified Korteweg – de Vries equation (α = 3, 2) and the Shamelle equation (α = 3/2, 3) in the case of uniform distribution of amplitudes in the interval [0¸1]. ρ = 1/30.

下载 (57KB)
索引源数据

版权所有 © Russian Academy of Sciences, 2025