Related papers: Amplitude Equations for Electrostatic Waves: multi…
The anomalous scaling phenomena of three-dimensional passive scalar turbulence are studied using high resolution direct numerical simulation. The inertial range scaling exponents of the passive scalar increment and the scalar dissipation…
We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We…
Atmospheres having a significant radiative support are shown to be intrinsically unstable at luminosities above a critical fraction Gamma_crit ~ 0.5-0.85 of the Eddington limit, with the exact value depending on the boundary conditions. Two…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
Electron acoustic waves (EAWs) are nonlinear plasma modes characterized by electron trapping, which suppresses the usual Landau damping. Despite being predicted in the 1990s, their excitation and decay mechanisms remain a subject of active…
Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
Perpendicular electron dynamics and the associated collisions are discussed in relation to the collisional drift wave instability. In addition, the limit of small parallel wave numbers of this instability is studied and it is shown to yield…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
The present work shows that essentially all small-amplitude periodic traveling waves of the electronic Euler-Poisson system are spectrally unstable. This instability is neither modulational nor co-periodic, and thus requires an unusual…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
We study the instability of standing-wave solutions $e^{i\omega t}\phi_{\omega}(x)$ to the inhomogeneous nonlinear Schr\"{o}dinger equation $$i\phi_t=-\triangle\phi+|x|^2\phi-|x|^b|\phi|^{p-1}\phi, \qquad \in\mathbb{R}^N, $$ where $ b > 0 $…
In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated…
Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing.…
Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are…
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as $t$ goes to the infinity more slowly than any…
A freely falling stream of weakly cohesive granular particles is modeled and analysed with help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a…
The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed…