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In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT). We revise WT theory using a generalisation of the random phase approximation (RPA). This…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…
We analyze a set of bidirectional wave experiments in a linear wave flume of which some are conducive to integrable turbulence. In all experiments the wavemaker forcing is sinusoidal and the wave motion is recorded by seven high-resolution…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
We study numerically the nonlinear stage of modulational instability (MI) of cnoidal waves, in the framework of the focusing one-dimensional Nonlinear Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of the NLS…
We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong…
We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{\"o}dinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation…
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water…
The concept of Nonlinear dispersion relation (NDR) is used in various fields of Physics (nonlinear optics, hydrodynamics, hydroelasticity, mechanics, quantum optics, plasma physics,...) to characterize fundamental phenomena induced by…
We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
The nonlinear Schr\"odinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear…
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model based on the non-linear Schrodinger equation…
We consider a generic Hamiltonian system of nonlinear interacting waves with 3-wave interactions. In the kinetic regime of wave turbulence, which assumes weak nonlinearity and large system size, the relevant observable associated with the…
High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic…
Paraxial propagation of a quasi-monochromatic light wave with two circular polarizations in a defocusing Kerr medium with anomalous dispersion inside a waveguide of annular cross-section was considered. In the phase-separated mode, the…
Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a…
We theoretically investigate the solitary waves and their switching dynamics in a $\mathcal{PT}$-symmetric directional fiber coupler, exhibiting Kerr nonlinearity, by developing a variational analysis. We analyze the fundamental switching…