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Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability
Andrey Gelash1,2, Dmitry Agafontsev1,3, Vladimir Zakharov1,4
1Skolkovo Institute of Science and Technology, 121205, Moscow, Russia.
Physical Review Letters
|December 24, 2019
Summary
This study explains the theoretical basis for noise-induced modulational instability (MI) using soliton solutions. The findings show remarkable agreement between theoretical models and numerical simulations of MI evolution.
Area of Science:
- Nonlinear physics
- Wave phenomena
- Statistical mechanics
Background:
- Modulational instability (MI) is a key phenomenon in nonlinear wave systems.
- Previous observations of noise-induced MI lacked a comprehensive theoretical explanation.
- The statistical properties of MI have been noted in simulations and experiments.
Purpose of the Study:
- To develop a theoretical model for the asymptotic stage of noise-induced MI.
- To explain the statistical properties of spontaneous, noise-induced MI.
- To connect MI dynamics to integrable turbulence.
Main Methods:
- Utilized the inverse scattering transform (IST) formalism.
- Employed N-soliton solutions of the nonlinear Schrödinger equation.
- Constructed ensembles of multisoliton bound states with random phases.
Main Results:
- Proposed a theoretical model for noise-induced MI based on N-soliton solutions.
- Demonstrated agreement between spectral/statistical properties of MI and multisoliton states.
- Verified the model using a large-N (N∼100) soliton ensemble.
Conclusions:
- The theoretical model successfully explains the statistical properties of noise-induced MI.
- The findings bridge the gap between theoretical predictions and experimental observations.
- Results are generalizable to other nonlinear integrable turbulence problems.
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