Related papers: Complete Solution of Hadamard's Problem for the Sc…
We prove that if the non-self-adjoint scalar wave equation satisfies Huygens' principle on Petrov type III space-times, then it is equivalent to the conformally invariant scalar wave equation.
Extending previous results we show that there are no Petrov type III space-times on which either the Weyl neutrino equation or Maxwell's equations satisfy Huygens' principle. We prove the result by using Maple's NPspinor package to convert…
All classes of spatially homogeneous space-time models in the generalized scalar-tensor theory of gravity are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of %complete…
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated…
Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like space-time models allow the existence of privileged coordinate systems where the…
Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space-time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the…
Huygens triviality-a concept invented by Jacques Hadamard-describes an equivalence class connecting those 2nd order partial differential equations which are transformable into the wave equation. In this work it is demonstrated, that the…
We propose a novel Hadamard integrator for the self-adjoint time-dependent wave equation in an inhomogeneous medium. First, we create a new asymptotic series based on the Gelfand-Shilov function, dubbed Hadamard's ansatz, to approximate the…
For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a privileged coordinate system, where the…
We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the…
Motivated by the study of small amplitudes non-linear waves in the Anti-de-Sitter spacetime and in particular the conjectured existence of periodic in time solutions to the Einstein equations, we construct families of arbitrary small…
Type N spacetimes of the Kundt class are presented as solutions to Einstein's equations sourced by a real scalar field whose equation of motion is conformally invariant and that generalizes the standard conformal scalar field. The specific…
We study exact vacuum solutions to quadratic gravity (QG) of the Weyl types N and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type N with an appropriately chosen effective cosmological constant $\Lambda$…
We prove the nonexistence of local self-similar solutions of the three dimensional incompressible Navier-Stokes equations. The local self-similar solutions we consider here are different from the global self-similar solutions. The…
In this work, we obtain all spatially homogeneous space-time models related to the intersection of the set of St\"ackel spaces of type (2.1) and the set of conformally St\"ackel spaces of type (3.1). These models allow a complete separation…
We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations…
We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation…
I find nearly plane-wave solutions for the Gauss-Ampere law for the 4-vector potential, subject to the Lorenz gauge condition, in the spacetime of a plane gravitational plane wave. I assume that the gravitational wave is weak, in the sense…
There is a theorem known as a Virial theorem that restricts the possible existence of non-trivial static solitary waves with scalar fields in a flat space-time with 3 or more spatial dimensions. This raises the following question: Does the…
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with…