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We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
In this work, a systematic study, examining the propagation of periodic and solitary wave along the magnetic field in a cold collision-free plasma, is presented. Employing the quasi-neutral approximation and the conservation of momentum…
In this article, we use the general theory derived in the companion paper [M. Tacu and D. B\'enisti, Phys. Plasmas (2021)] in order to address several long-standing issues regarding nonlinear electron plasma waves (EPW's). First, we discuss…
We present a novel numerical scheme for the efficient and accurate solution of the isothermal two-fluid (electron and ion) equations coupled to Poisson's equation for low-temperature plasmas. The model considers electrons and ions as…
We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order.…
We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…
The propagation of nonlinear electron- acoustic waves (EAWs) in an unmagnetized collision- less plasma system consisting of a cold electron fluid, superthermal hot electrons and stationary ions is investigated. A reductive perturbation…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
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…
Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide…
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the…
This paper addresses the linear propagation of an electron wave in a collisionless, inhomogeneous, nonstationary and anisotropic plasma. The plasma is characterized by its distribution function, $f_H$, at zero order in the wave amplitude.…
A novel time domain solver of Maxwell's equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of ({\it i}) the Hamiltonian formalism and…
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions,…
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general…
We employ the Sagdeev pseudo-potential method to investigate the propagation of nonlinear ion waves in a relativistically degenerate electron-ion plasmas. The matching criteria for existence of such nonlinear excitations are numerically…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…