相关论文: Propagation of instability fronts in modulationall…

We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with the inverse linear dispersion law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave number, and…

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…

Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear…

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

A nonresonant cosmic-ray-current-driven instability may operate in the shock precursors of young supernova remnants and be responsible for magnetic-field amplification, plasma heating and turbulence. Earlier simulations demonstrated…

We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have…

We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…

The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during…

A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in…

This paper is concerned with the spatial propagation of nonlocal dispersal equations with bistable or multistable nonlinearity in exterior domains. We obtain the existence and uniqueness of an entire solution which behaves like a planar…

The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms…

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…

In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…

In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in…

We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization,…

In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, we prove the exponential behavior of pushed fronts when they are…

Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…

In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions evolve towards a planar travelling wave modulated by a…

We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…