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Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability. / Gelash, Andrey; Agafontsev, Dmitry; Zakharov, Vladimir et al.

In: Physical Review Letters, Vol. 123, No. 23, 234102, 06.12.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Gelash, A, Agafontsev, D, Zakharov, V, El, G, Randoux, S & Suret, P 2019, 'Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability', Physical Review Letters, vol. 123, no. 23, 234102. https://doi.org/10.1103/PhysRevLett.123.234102

APA

Gelash, A., Agafontsev, D., Zakharov, V., El, G., Randoux, S., & Suret, P. (2019). Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability. Physical Review Letters, 123(23), [234102]. https://doi.org/10.1103/PhysRevLett.123.234102

Vancouver

Gelash A, Agafontsev D, Zakharov V, El G, Randoux S, Suret P. Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability. Physical Review Letters. 2019 Dec 6;123(23):234102. doi: 10.1103/PhysRevLett.123.234102

Author

Gelash, Andrey ; Agafontsev, Dmitry ; Zakharov, Vladimir et al. / Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability. In: Physical Review Letters. 2019 ; Vol. 123, No. 23.

BibTeX

@article{df1d0e30207a4ddc9d711976160e49c1,
title = "Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability",
abstract = "We investigate the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The statistical properties of the noise-induced MI, observed previously in numerical simulations and in experiments, have not been explained theoretically. In this Letter, using the inverse scattering transform (IST) formalism, we propose a theoretical model of the asymptotic stage of the noise-induced MI based on N-soliton solutions of the focusing one-dimensional nonlinear Schr{\"o}dinger equation. Specifically, we use ensembles of N-soliton bound states having a special semiclassical distribution of the IST eigenvalues, together with random phases for norming constants. To verify our model, we employ a recently developed numerical approach to construct an ensemble of N-soliton solutions with a large number of solitons, N∼100. Our investigation reveals a remarkable agreement between spectral (Fourier) and statistical properties of the long-term evolution of the MI and those of the constructed multisoliton, random-phase bound states. Our results can be generalized to a broad class of strongly nonlinear integrable turbulence problems.",
keywords = "INTEGRABLE TURBULENCE, SELF-MODULATION, STATISTICS, RECURRENCE, EQUATIONS, TRAINS, WAVES, PHASE",
author = "Andrey Gelash and Dmitry Agafontsev and Vladimir Zakharov and Gennady El and St{\'e}phane Randoux and Pierre Suret",
year = "2019",
month = dec,
day = "6",
doi = "10.1103/PhysRevLett.123.234102",
language = "English",
volume = "123",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "23",

}

RIS

TY - JOUR

T1 - Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability

AU - Gelash, Andrey

AU - Agafontsev, Dmitry

AU - Zakharov, Vladimir

AU - El, Gennady

AU - Randoux, Stéphane

AU - Suret, Pierre

PY - 2019/12/6

Y1 - 2019/12/6

N2 - We investigate the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The statistical properties of the noise-induced MI, observed previously in numerical simulations and in experiments, have not been explained theoretically. In this Letter, using the inverse scattering transform (IST) formalism, we propose a theoretical model of the asymptotic stage of the noise-induced MI based on N-soliton solutions of the focusing one-dimensional nonlinear Schrödinger equation. Specifically, we use ensembles of N-soliton bound states having a special semiclassical distribution of the IST eigenvalues, together with random phases for norming constants. To verify our model, we employ a recently developed numerical approach to construct an ensemble of N-soliton solutions with a large number of solitons, N∼100. Our investigation reveals a remarkable agreement between spectral (Fourier) and statistical properties of the long-term evolution of the MI and those of the constructed multisoliton, random-phase bound states. Our results can be generalized to a broad class of strongly nonlinear integrable turbulence problems.

AB - We investigate the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The statistical properties of the noise-induced MI, observed previously in numerical simulations and in experiments, have not been explained theoretically. In this Letter, using the inverse scattering transform (IST) formalism, we propose a theoretical model of the asymptotic stage of the noise-induced MI based on N-soliton solutions of the focusing one-dimensional nonlinear Schrödinger equation. Specifically, we use ensembles of N-soliton bound states having a special semiclassical distribution of the IST eigenvalues, together with random phases for norming constants. To verify our model, we employ a recently developed numerical approach to construct an ensemble of N-soliton solutions with a large number of solitons, N∼100. Our investigation reveals a remarkable agreement between spectral (Fourier) and statistical properties of the long-term evolution of the MI and those of the constructed multisoliton, random-phase bound states. Our results can be generalized to a broad class of strongly nonlinear integrable turbulence problems.

KW - INTEGRABLE TURBULENCE

KW - SELF-MODULATION

KW - STATISTICS

KW - RECURRENCE

KW - EQUATIONS

KW - TRAINS

KW - WAVES

KW - PHASE

UR - http://www.scopus.com/inward/record.url?scp=85076728914&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.123.234102

DO - 10.1103/PhysRevLett.123.234102

M3 - Article

C2 - 31868438

AN - SCOPUS:85076728914

VL - 123

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 23

M1 - 234102

ER -

ID: 23094167