Related papers: Space Propagation of Instabilities in Zakharov Equ…
We show in experiments that a long, underdense, relativistic proton bunch propagating in plasma undergoes the oblique instability, that we observe as filamentation. We determine a threshold value for the ratio between the bunch transverse…
We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess Gaussian probability density function and establish quantitative criteria…
With the increasing use of ultrashort laser pulses and nanoscale-materials, one is regularly confronted to situations in which the properties of the media supporting propagation are not varying slowly with time (or space). Hence, the usual…
We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that the Cauchy problem is well posed in anisotropic…
We study the tearing instability of a current sheet in a relativistic pair plasma with a power law distribution function. We first estimate the growth rate analytically and then confirm the analytical results by solving numerically the…
Extreme states of matter exist throughout the universe e.g. inside planetary cores, stars or astrophysical jets. Such conditions are generated in the laboratory in the interaction of powerful lasers with solids, and their evolution can be…
Because the initial shape of the QGP in a heavy ion collision is anisotropic, the momentum distribution becomes anisotropic after a short time. This leads to plasma instabilities, which may help explain how the plasma isotropizes. We…
We investigate beam diffraction and spatial modulation instability of coherent light beams propagating in the non-paraxial regime in a nonlinear Kerr medium. We study the instability of plane wave solutions in terms of the degree of…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming the initial datum is localized with respect to a coordinate having slow diffusion rate,…
The instability of a monoenergetic electron beam in a collisional one-dimensional plasma bounded between grounded walls is considered both analytically and numerically. Collisions between electrons and neutrals are accounted for the plasma…
When a relativistic intensity laser interacts with the surface of a solid density target, suprathermal electron currents are subject to Weibel instability filamentation when propagating through the thermal population of the bulk target. We…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
In the present paper the linearized problem of plasma oscillations in slab (particularly, thin films) in external longitudinal alternating electric field is solved analytically. Specular boundary conditions of electron reflection from the…
We consider a Vlasov equation for a plasma with a given constant magnetic field, and introduce a white noise perturbation of the electric field in the electrostatic approximation, with a discussion of the motivations of such random…
The initial value problem for two-dimensional Zakharov-Kuznetsov equation on periodic boundary setting is shown to be locally well-posed in the cylinder for 9/10 < s < 1. We prove this theorem by using bilinear estimates thinking separetely…
{Using two different approaches, we study imaging in the strong lens regime taking into account the effects of plasmatic environments on light propagation. First, we extend the use of a perturbative approach that allows us to quickly and…
The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…