Related papers: Self-accelerating Parabolic Cylinder Waves in 1-D
A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys. \textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schr\"odinger equation is presented. Equations are further simplified and generalized for computing wave…
We derive a new integral equation that allows the calculation of the scattering or annihilation amplitude of two particles subjected to two potentials when the corresponding amplitude for one potential only is known. We assume that…
Self-accelerating beams are fascinating solutions of the Schr\"odinger equation. Thanks to their particular phase engineering, they can accelerate without the need of external potentials or applied forces. Finite-energy approximations of…
We present the first experimental observation of accelerating beams in curved space. More specifically, we demonstrate, experimentally and theoretically, shape-preserving accelerating beams propagating on spherical surfaces: closed-form…
Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
In this paper we consider three different 1D parabolic-parabolic systems of chemotaxis. For these systems we obtain the exact analytical solutions in terms of traveling wave variables.
The convergence of the so-called quadratic method for computing eigenvalue enclosures of general self-adjoint operators is examined. Explicit asymptotic bounds for convergence to isolated eigenvalues are found. These bounds turn out to…
The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
In this paper, we use the variational method to find the normalized solutions of the quadratic coupled three wave Schrodinger equation with asymmetric coercive potential. We prove the existence of solutions for the system with 2-norm…
Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…
Electromagnetic waves, in vacuum or dielectrics, can be confined in unbounded cylinders in such a way that they turn around the main axis. For particular choices of the cylinder's section, interesting stationary configurations may be…
In this paper, we study self-expanding solutions to a large class of parabolic inverse curvature flows by homogeneous symmetric functions of principal curvatures in Euclidean spaces. These flows include the inverse mean curvature flow and…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic equation. In the usual kinetic limit, the resulting…
The general form of the cubic Boussinesq-type equation is considered. In special cases, this equation is reduced to the three different versions of the cubic Boussinesq equations and also the generalized modified cubic Boussinesq equation.…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…