相关论文: Quaternionic fundamental solutions for the numeric…

The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…

Dual electrodynamics and corresponding Maxwell's equations (in the presence of monopole only) are revisited from dual symmetry and accordingly the quaternionic reformulation of field equations and equation of motion is developed in simple,…

We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless…

A first-order elliptic-hyperbolic system in extended projective space is shown to possess strong solutions to a natural class of Guderley-Morawetz-Keldysh problems on a typical domain.

We establish the local wellposedness of different type of solutions the system with different types of initial data. We find there exists a critical exponents line in space dimension 3 and critical exponents point in space dimension 4. We…

A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…

In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is…

Foundations of algebrodynamics based on earlier proposed equations of biquaternionic holomorphy are briefly expounded. Free Maxwell and Yang-Mills Eqs. are satisfied identically on the solutions of primary system which is also related to…

The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…

In quantum theory, the so-called "spinless Salpeter equation," the relativistic generalization of the nonrelativistic Schroedinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound…

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…

Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying the causality principle is obtained which allows us to solve…

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…

We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient…

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…

In this paper, we present a new method for solving standard quaternion equations. Using this method we reobtain the known formulas for the solution of a quadratic quaternion equation, and provide an explicit solution for the cubic…

A formalism based on the complex-scaling method is presented to solve the few particle scattering problem in configuration space using bound state techniques with trivial boundary conditions. Several applications to A=3,4 systems are…

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…

Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…

We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…