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The integrability nature of a nonparaxial nonlinear Schr\"odinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlev\'e singularity structure…
The nonlinear coupling between the light beams and non-resonant ion density perturbations in a plasma is considered, taking into account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations…
We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…
The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to…
The self-action features of wave packets propagating in a two-dimensional system of equidistantly arranged fibers are studied analytically and numerically on the basis of the discrete nonlinear Schr\"odinger equation. Self-consistent…
We propose a nonlinear self-consistent model of the turbulent non-resonant particle acceleration in solar flares. We simulate temporal evolution of the spectra of charged particles accelerated by strong long-wavelength MHD turbulence taking…
The properties of obliquely propagating dissipative electron-acoustic solitary waves (OPdEASWs) have been investigated in a magnetized collisional superthermal plasma consisting of inertial cold electrons, inertialess hot electrons…
Nonlinear propagation of electrostatic modes in ultrarelativistic dense elelectron-positron gravito-plasma at the polar cap region of pulsar magnetosphere is considered. A nonlinear Schr\"{o}dinger equation is obtained from the reductive…
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the…
In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian…
In this research, numerical analysis of nonlinear pulse propagation is carried out. This is done mainly by solving the nonlinear Schrodinger equation using the split step algorithm. In a nonlinear media, dispersive effects exist…
The self-consistent problem of the wave and particle spectrum is formulated and solved for acceleration of particles in a homogeneous magnetic field that varies periodically with time. It follows from the obtained solutions that when…
We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…
The condition for potential description of the wake waves,generated by flat or cylindrical driving electron bunch in cold plasma is derived. The two-dimensional nonlinear equation for potential valid for small values of that is obtained and…
In this paper, an inverse variational problem is solved for the nonlocal nonlinear Schrdinger equation used in modeling filamentation in various nonlinear media. The corresponding integral relations are found which generalize the…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…
Thermal Wave Model is used to study the strong self-consistent Plasma Wake Field interaction (transverse effects) between a strongly magnetized plasma and a relativistic electron/positron beam travelling along the external magnetic field,…
We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…