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Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is…
This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is…
In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a…
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example,…
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction…
We present a method how to estimate from experimental data of a turbulent velocity field the drift and the diffusion coefficient of a Fokker-Planck equation. It is shown that solutions of this Fokker-Planck equation reproduce with high…
We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal,…
In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect…
Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this…
We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one-dimensional Schr\"odinger-like equation with a barrier-type potential. Using numerical methods, we…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…
We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…