Related papers: Split octonions and Maxwell equations
We present a theoretical derivation of the homogenous Maxwell equations, based on Stokes theorem for Minkowski space tensors.
Unlike the Hamilton quaternion algebra, the split-quaternions contain nontrivial zero divisors. In general speaking, it is hard to find the solutions of equations in algebras containing zero divisor. In this paper, we manage to derive…
Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…
We propose a simple quaternionic reformulation of Maxwell's equations for inhomogeneous media and use it in order to obtain new solutions in a static case.
In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
We give a gentle introduction to Frobenius splittings. Then we recall a few results that have been obtained with the method.
A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…
In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…
We give description of rational solutions of polynomial-equations.
A procedure to teach Electrodynamics independently of unit systems is presented and compared with some of those given in physics literature.
Computations in the cohomology of finite groups.
We give a concise direct proof of the orthogonality of interpolation Macdonald polynomials with respect to the Fourier pairing and briefly discuss some immediate applications of this orthogonality, such as the symmetry of the Fourier…
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…
In this paper we study certain quaternion algebras and symbol algebras which split.
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…