Related papers: Nonlinear Maxwell Equations
The relativistic quantum mechanics equations for the electromagnetic interaction are propososed.
We consider the one and one-half dimensional multi-species relativistic Vlasov-Maxwell system with non-decaying(in space) initial data. We prove its well-posedness and nonrelativistic limit as the speed of light $c\rightarrow\infty$. These…
The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of…
Several complementary approaches to investigate knotted solutions of Maxwell's equations in vacuum are now available in literature. However, only partial results towards a unified description of them have been achieved. This is potentially…
The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity is revisited by a relatively direct way with a pointwise estimate of fractional derivative of some test functions.
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
By using the quantum hydrodynamic and Maxwell equations, we derive nonlinear electron-magnetohydrodynamic (MHD), Hall-MHD, and dust Hall-MHD equations for dense quantum magnetoplasmas. The nonlinear equations include the electromagnetic,…
Application of the noncommutative geometry to several physical models is considered.
In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These…
This paper studies non-linear constitutive equations for gravitoelectromagnetism. Eventually, the problem is solved of finding, for a given particular solution of the gravity-Maxwell equations, the exact form of the corresponding non-linear…
Relativistic complex Burgers-Schr\"odinger and Nonlinear Schr\"odinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
We consider the question of linear instability of an equilibrium of the Relativistic Vlasov-Maxwell (RVM) System that has a strong magnetic field. Standard instability results deal with systems where there are fewer particles with higher…
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are…