In this letter we describe a new and simple approach for modulating the electromagnetic wave propagating in a dielectric medium in the form of solitons by considering the torque developed between the induced dipoles in the medium and external field without taking into account the nonlinear Kerr effect. A reductive perturbation method deduces the Maxwell equation coupled with the Larmor equation...

We investigate the quantum Vlasov equation with a source term describing the spontaneous particle creation in strong fields. The back-reaction problem is treated by solving this kinetic equation together with the Maxwell equation which determines the induced time-dependent electric field in the system. The evolution of distribution functions for bosons and fermions is studied numerically. We fo...

The most efficient solvers for finite element (fe) equations are certainly multigrid, or multilevel methods, and domain decomposition methods using local multigrid solvers. Typically, the multigrid convergence rate is independent of the mesh size parameter, and the arithmetical complexity grows linearly with the number of unknowns. However, the standard multigrid algorithms fail for the Maxwell...

We deal with the propagation of broadband Schell-model sources in nonlinear media with finite relaxation time. The approach is based on a study of the Wigner distribution function and on a separation of scales technique between the microscopic random fluctuations of the field and the macroscopic intensity profile. The regime in which the nonlinearity is strong and slow is considered. Precise re...

Recently a wave equation for unified field theory has been derived [1-3] from a lemma of Cartan-Riemann differential geometry [4, 5] and used to give the first self consistent unified description of the gauge invariant gravitational and electromagnetic fields. The former is the Riemann form and the latter is the torsion form. One form is the Hodge dual of the other. The theory has been shown [1...

It is well-known that a conflict between Galilean relativity and Maxwell equations of electromagnetic equations was apparent by the end of the 19th century. Equally well-known is the fact that Einstein resolved the conflict by pointing out that the principle of relativity and Maxwell equations can both be correct if the notion of absolute time is abandoned. The rest is history. The purpose of t...

The present author has postulated a 4-dimensional (4D) aether formed by a fluid of preons in continual motion in a 4D-space (w,x,y,z), where the time dimension w is treated exactly the same as the spatial dimensions. By specializing the equation of motion to an inviscid constant density region of 4D moving with speed c along the w-axis, we obtain Maxwell equations and the associated continuity ...

We consider solutions of the non-linear von Neumann equation involving Jacobi’s elliptic functions sn, cn, and dn, and 3 linearly independent operators. In two cases one can construct a state-dependent Hamiltonian which is such that the corresponding non-linear von Neumann equation is solved by the given density operator. We prove that in a certain context these two cases are the only possibili...

1. Linearity and Continuity 1.1 Continuity 1.2 Linearity 1.3 Perturbation theory and linearity 1.4 Axiomatically linear equations 1.4.1 Fields, Maxwell equations 1.4.2 Densities on phase space in classical physics 1.4.3 Quantum mechanics and Schrödinger equation 2. Examples 2.1 Ordinary differential equations 2.2 The Laplace equation 2.3 The wave equation 2.4 The heat equation and Schrödinger e...

In this note we study the temporal convergence of a locally implicit discontinuous Galerkin (DG) method for Maxwell’s equations modeling electromagnetic wave propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) sol...