Related papers: Radially Self-Accelerating Beams
We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in $\mathbb{R}^N$ with bistable, ignition or monostable nonlinearities that exhibit threshold behavior. For $L^2$ initial…
A review of a recent theoretical investigation of the quantum transverse beam motion that has been developed in terms of a coupled system of nonlinear spinorial equations is carried out. This is done assuming that a relativistic…
The new symmetry axis of a well-behaved electromagnetic beam advanced in paper Physical Review A 78, 063831 (2008) is not purely a mathematical concept. The experimental result reported by Hosten and Kwiat in paper Science 319, 787 (2008)…
In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained…
We describe the accelerated propagation wave arising from a non-local reaction-diffusion equation. This equation originates from an ecological problem, where accelerated biological invasions have been documented. The analysis is based on…
An electron irradiated by a linearly polarized relativistic intensity laser pulse in a cylindrical plasma channel can gain significant energy from the pulse. The laser electric and magnetic fields drive electron oscillations in a plane…
Self modulated dynamics of a relativistic charged particle beam is reviewed within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation…
We report a new form of compensating accelerating beam generated by amplitude modulation of the symmetric Airy beam (SAB) caustics with an exponential apodization mask. Our numerical study manifests that the compensating beam is with one…
The existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. The fourth-order radial equation is non-self adjoint and has no exact solutions.…
Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index $n$…
In this letter, we introduce a new class of light beam, the circular symmetric Airy beam (CSAB), which arises from the extensions of the one dimensional (1D) spectrum of Airy beam from rectangular coordinates to cylindrical ones. The CSAB…
Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…
We consider the wave-structure coupling between an orbital angular momentum beam and a rapidly rotating disk, and present a new configuration exhibiting the wave amplification effect known as rotational superradiance. While initially…
The propagation characteristics of Airy beams is investigated and fully described under the traveling waves approach analogous to that used for non-diffracting Bessel beams. This is possible when noticing that Airy functions are in fact…
The exact quantum-mechanical equations for beams of free particles including photons and for beams of Dirac and spin-1 particles in a uniform magnetic field have been derived. These equations present the exact generalizations of the…
We address the propagation of vortex beams with the circular Airy-Gaussian shape in a (2+1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation. Systematic analysis of autofocusing of the beams reveals a…
We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general…
The acceleration of charged particles at astrophysical collisionless shock waves is one of the best studied processes for the energization of particles to ultrarelativistic energies, required by multifrequency observations in a variety of…
Self-healing, as an exotic effect, has showed many potential applications. In this paper, we focus on the self-healing effect of Laguerre-Gaussian beams after an obstacle. By taking advantage of angular spectrum theory, we study…
We study the dynamics of active Janus particles that self-propel in solution by light-activated catalytic decomposition of chemical "fuel." We develop an analytical model of a photo-active self-phoretic particle that accounts for…