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 -