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
N1 - Funding Information:
The authors thank A. Tikan and F. Copie for fruitful discussions. Simulations were performed at the Novosibirsk Supercomputer Center (NSU). This work has been partially supported by the Agence Nationale de la Recherche through the LABEX CEMPI Project (Project No.ANR-11-LABX-0007) and the I-SITE ULNE (ANR-16-IDEX-004) and by the Ministry of Higher Education and Research, Hauts-De-France Regional Council and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-Region (CPER Photonics for Society Grant No.P4S). The work on the construction of multisoliton ensembles reported in the first half of the Letter was supported by the Russian Science Foundation (Grant No.19-72-30028 to A.G., D.A., and V.Z.). The work of G.E. was partially supported by EPSRC Grant No.EP/R00515X/2.
Publisher Copyright:
© 2019 American Physical Society.
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.
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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 -