Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability

Andrey Gelash, Dmitry Agafontsev, Vladimir Zakharov, Gennady El, Stéphane Randoux, Pierre Suret

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

24 Цитирования (Scopus)


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.

Язык оригиналаанглийский
Номер статьи234102
Число страниц7
ЖурналPhysical Review Letters
Номер выпуска23
СостояниеОпубликовано - 6 дек 2019


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