We discover that, at the edge of an optical lattice imprinted in a saturable nonlinear medium, one-dimensional surface solitons exist only within a band of light intensities and that they cease to exist when the lattice depth exceeds an upper threshold. We also reveal the generation of arrays of two-dimensional surface solitons mediated by the transverse modulational instability of one-dimensio...

Nonlinear solitary structures of electron plasma waves have been investigated by using nonlinear quantum fluid equations for electrons with an arbitrary temperature. It is shown that the electron degeneracy parameter has significant effects on the linear and nonlinear properties of electron plasma waves. Depending on its value both compressive and rarefactive solitons can be excited in the mode...

The quantum methodologies useful for describing in a unified way several problems of nonlinear and collective dynamics of fluids, plasmas and beams are presented. In particular, the pictures given by the Madelung fluid and the Moyal-Ville-Wigner phase-space quasidistribution, including the related quantum tools such as marginal distributions for the tomographic representations, are described. S...

Experimental evidence for the generation of intrinsic localized modes (ILMs) in a nonlinear electrical transmission line is presented both via modulational instability of the uniform mode and via driving the lattice locally. The spatial profiles of these modes localized on the order of the lattice spacing can be directly measured in this macroscopic lattice, in contrast to most other systems wh...

Localized modes are analysed for a chain with nonlinear on-site potential using an approximation based on the discrete nonlinear Schr0dinger equation. It is pointed out that such localized modes exist in the parameter domains where the system displays modulational instability. Otherwise, nonlinear modes may appear in the form of dark-profile localized structures, and two types of such structure...

A dispersive Landau-fluid model is used to study the decay and modulational instabilities of circularlypolarized Alfvén waves in a collisionless plasma, as well as their nonlinear developments. Comparisons are presented with the drift-kinetic approximation for the dispersionless regime and with hybrid simulations in more general conditions. The effect of the nature of the instability on particl...

We present a theory for the generation of mesoscale (kr g ≪ 1, where r g is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mecha...

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the twodimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variation...

On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwid...

Quasilinear diffusion due to modulational instability is considered in this paper. Interaction between the high-frequency, nearly transverse O mode (or the transverse X mode) and the low-frequency, nearly longitudinal L-O mode in a pulsar magnetospheric pair plasma can lead to modulational instability. The low-frequency L-O mode is superluminal, which is not subjected to usual Landau damping, a...