Related papers: Improved Numerical Method for Solution of the Ha\"…
The procedure of comprehensive analysis of instability of current sheathes in a wide range of frequencies and wave lengths in the electrically neutral approximation has been developed. This comprehensive analysis of instability is based on…
New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation…
Excited states of Bose--Einstein condensates are considered in the semi-classical (Thomas-Fermi) limit of the Gross--Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark…
The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact…
The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation…
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…
It is shown that hyperspherical harmonics can be represented in a form typical of traditional microscopic cluster models. This allows those hyperharmonics that are responsible for long-range behaviour of valence nucleons in loosely-bound…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic…
I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent…
Self modulated dynamics of a relativistic charged particle beam is reviewed within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation…
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral stability criterion and the formal stability criterion in the form of necessary and…
We study the relaxation to equilibrium for a class linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for…
This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We study long-time dynamical behaviors of weakly self-consistent Vlasov-Fokker-Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which characterizes the exponential convergence of solutions in $L^1$…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…