Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability

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

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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.

Original languageEnglish (US)
Article number234102
JournalPhysical review letters
Issue number23
StatePublished - Dec 6 2019

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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