Related papers: Approximated solutions to Born-Infeld dynamics
We consider scalar Born-Infeld type theories with arbitrary potentials V(T) of a scalar field T. We find that for models with runaway potentials V(T) the generic inhomogeneous solutions after a short transient stage can be very well…
We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of…
The generalized Born--Infeld electrodynamics with two parameters is investigated. In this model the propagation of a linearly polarized laser beam in the external transverse magnetic field is considered. It was shown that there is the…
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find…
This article is devoted to studying the inverse scattering for the fractional Schr\"{o}dinger equation, and in particular we solve the Born approximation problem. Based on the ($p$,$q$)-type resolvent estimate for the fractional Laplacian,…
We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion…
We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
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…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
We compute the Bohmian trajectories of the incoming scattering plane waves for Klein's potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…