Related papers: Evolution and statistical analysis of random wave …
In this paper, we give the first rigorous justification of the Benjamin-Ono equation as an internal water wave model on the physical time scale. Let $\varepsilon$ be the small parameter measuring the weak nonlinearity of the waves, $\mu$ be…
Considered here are two systems of equations modeling the two-way propagation of long-crested, long-wavelength internal waves along the interface of a two-layer system of fluids in the Benjamin-Ono and the Intermediate Long-Wave regime,…
The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background…
Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here,…
We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time-evolution of optical and matter-wave fields is performed in the…
We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the…
Numerical simulations are used to discuss various aspects of "optical rogue wave" statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength…
The proplem of sound propagation in an oceanic waveguide is considered. Scattering on random inhomogeneity of the waveguide leads to wave chaos. Chaos reveals itself in spectral properties of the finite-range evolution operator (FREO). FREO…
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main…
Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…
In this work, we study numerically the temporal evolution of an initially random large-scale velocity field under governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution.…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an $r^{-2}$ repulsive potential. Analysis of both stationary wave fields and transient transport…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from…
In the seminal work of Benjamin,\cite{Ben} in the late 70's, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum.…
We study the intersection points of a fixed planar curve $\Gamma$ with the nodal set of a translationally invariant and isotropic Gaussian random field $\Psi(\bi{r})$ and the zeros of its normal derivative across the curve. The intersection…
Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…