Soliton gas: Theory, numerics, and experiments.

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted (rarefied) soliton gas, solitons with random amplitude and phase parameters are almost nonoverlapping. More recently, the concept has been extended to dense gases in which solitons strongly and continuously interact.

Solitonic model of the condensate.

We consider a spatially extended box-shaped wave field that consists of a plane wave (the condensate) in the middle and equals zero at the edges, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. Within the inverse scattering transform theory, the scattering data for this wave field is presented by the continuous spectrum of the nonlinear radiation and the soliton eigenvalues together with their norming constants; the number of solitons N is proportional to the box width. We remove the continuous spectrum from the scattering data and find analytically the specific corrections to the soliton norming constants that arise due to the removal procedure.

Extreme rogue wave generation from narrowband partially coherent waves.

In the framework of the focusing one-dimensional nonlinear Schrödinger equation, we study numerically the integrable turbulence developing from partially coherent waves (PCW), which represent superposition of uncorrelated linear waves. The long-time evolution from these initial conditions is characterized by emergence of rogue waves with heavy-tailed (non-Gaussian) statistics, and, as was established previously, the stronger deviation from Gaussianity (i.e.

Bound State Soliton Gas Dynamics Underlying the Spontaneous Modulational Instability.

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.

Statistical Properties of the Nonlinear Stage of Modulation Instability in Fiber Optics.

We present an optical fiber experiment in which we examine the space-time evolution of a modulationally unstable plane wave initially perturbed by a small noise. Using a recirculating fiber loop as an experimental platform, we report the single-shot observation of the noise-driven development of breather structures from the early stage to the long-term evolution of modulation instability. Performing single-point statistical analysis of optical power recorded in the experiments, we observe decaying oscillations of the second-order moment together with the exponential distribution in the long-term evolution, as predicted by Agafontsev and Zakharov [Nonlinearity 28, 2791 (2015).