Related papers: Relativistic Approximate Solutions for a Two-Term …
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are…
A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections…
Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear differential and difference equations. Once such a equation…
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials $V_q(r)=-Z/\left(r^q+\beta^q\right)^{1/q}$, $Z>0$, $\beta>0$,…
In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…
We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the…
Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the…
The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound-state problem is the Klein-Fock-Gordon equation. In this…
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.
The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding…
In this work, on the condition that scalar potential is equal to vector potential, the bound state solutions of the Klein-Fock-Gordon equation of the Manning-Rosen plus ring-shaped like potential are obtained by Nikiforov-Uvarov method. The…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave…
In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent mass and speed of pro\-pagation. We introduce a classification of the potential term, which clarifies whether the solution…
Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these…
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…
We consider the damped nonlinear Klein-Gordon equation with a delta potential \begin{align*} \partial_{t}^2u-\partial_{x}^2u+2\alpha \partial_{t}u+u-\gamma {\delta}_0u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R}, \end{align*}…
This is the more technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with time-dependent coefficients, focusing on the Klein--Gordon…