Related papers: A new nonlinear generalization of the Dirac equati…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in $\mathbb{C}^{n}$ without any curvature assumptions on the domain.
We present various generalizations of the Dirac formalism. The different-parity solutions of the Weinberg's 2(2J+1)-component equations are found. On this basis, generalizations of the Bargmann-Wigner (BW) formalism are proposed. Relations…
Based on experimental evidences supporting the hypothesis that neutrinos might be tachyonic fermions, a new Dirac-type equation is proposed and a spin-1/2 tachyonic quantum theory is developed. The new Dirac-type equation provides a…
In case of spinless particles there appear additional (singular) solutions in the framework of relativistic Klein-Gordon equation for Coulomb potential. These solutions obey to all requirements of quantum mechanical general principles.…
We derive the semiclassical (with accuracy of $\hbar$) motion equation for relativistic electron, which follow from the Dirac equation. We determine both the evolution equation for electron polarization, which takes the non-Abelian Berry…
Based on the results of F. Wilf on the need to take into account the quantum-mechanical correspondence rules in the Dirac equation for an electron, it was shown that the equation obtained by giving physical meaning to $\alpha$-Dirac…
All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation.…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
We define and study the Cauchy problem for a 1-D nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws for mass and energy are shown. Several examples, including…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and…
The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the…
We derive a new unidirectional evolution equation for photonic nanowires made of silica. Contrary to previous approaches, our formulation simultaneously takes into account both the vector nature of the electromagnetic field and the full…
We proposed a new type of soliton equation, whose solutions may describe some statistical distributions, for example, Cauchy distribution, normal distribution and student distribution, etc. The equation possesses two characters. Further,…
We further generalize the powerful method, which we have recently developed for description of the background matter influence on neutrinos, for the case of an electron moving in matter. On the basis of the modified Dirac equation for the…
In the present article we present exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments. Using the algebraic method of separation of variables, the Dirac equation is separated in…
We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated…
Exact expression is obtained for the differential cross section of elastic electroweak scattering of longitudinal polarized massive Dirac neutrinos with the electric charge and anomalous magnetic moment on a spinless nucleus. This formula…