Related papers: Degenerate behavior in nonlinear vacuum electrodyn…
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the…
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron…
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum and the unitarity…
Plane waves in noncommutative classical electrodynamics (NCED) have a peculiar dispersion relation. We investigate the kinematical conditions on this deformed "mass shell" which come from ultra high energy gamma rays and discuss…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that…
Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of…
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…
The nonlinear propagation of low-frequency circularly polarized waves in a magnetized dusty plasma is analyzed. It is found that wave steepening and shock formation can take place due to the presence of nonlinear quantum vacuum effects,…
We consider a charged particle moving in a static electromagnetic field described by the vector potential $\vec A(\vec x)$ and the electrostatic potential $V(\vec x)$. We study the conditions on the structure of the integrals of motion of…
We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First, we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same…
In this paper, we investigate the formation and propagation of singularities for the system for one-dimensional Chaplygin gas, which is described by a quasilinear hyperbolic system with linearly degenerate characteristic fields. The…
Nonlinear electrodynamics has been an important area of research for a long time. Investigations based on nonlinear Lagrangians, such as Euler-Heisenberg and Born-Infeld, are instrumental in exploring the limits of classical and quantum…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
We study two counter--propagating electromagnetic waves in the vacuum within the framework of the Born--Infeld theory in quantum electrodynamics. By choosing the crossed field case ${\bf E}\cdot{\bf B}=0$, i.e. $\mathfrak{G}^2=0$, the…
Arbitrary amplitude nonlinear ion waves is investigated in an extremely degenerate electron-positron-ion plasma with relativistic electrons/positrons and dynamic cold ions using Sagdeev pseudo-potential method in framework of quantum…
We consider the Pleba{\'n}ski class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a…
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power…
For a class of nonlinear hyperbolic systems of second order the paper shows that all Lax modes associated with their first-order formulations are linearly degenerate. This property holds for recently considered models of dissipative…
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is…