Bound state soliton gas dynamics underlying the spontaneous modulational instability

Gelash, Andrey, Agafontsev, Dmitry, Zakharov, Vladimir, El, Gennady, Randoux, Stéphane and Suret, Pierre (2019) Bound state soliton gas dynamics underlying the spontaneous modulational instability. Physical Review Letters, 123 (23). p. 234102. ISSN 0031-9007

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Abstract

We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in experiments and in simulations but have not been explained so far. In the framework of inverse scattering transform (IST), we propose a model of the asymptotic stage of the noise-induced MI based on N-soliton solutions (N-SS) of the integrable focusing one-dimensional nonlinear Schrödinger equation (1D-NLSE). These N-SS are bound states of strongly interacting solitons having a specific distribution of the IST eigenvalues together with random phases. We use a special approach to construct ensembles of multi-soliton solutions with statistically large number of solitons N∼100. Our investigation demonstrates complete agreement in spectral (Fourier) and statistical properties between the long-term evolution of the condensate perturbed by noise and the constructed multi-soliton bound states. Our results can be generalised to a broad class of integrable turbulence problems in the cases when the wave field dynamics is strongly nonlinear and driven by solitons.

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