Related papers: Locally homogeneous pp-waves
The invariance of the phase of plane waves among inertial frames is investigated in some details. The reason that eventually led the author of a recent EPL letter [EPL \textbf{79}, 1006 (2007)] to a spurious conclusion of the non-invariance…
We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We prove the non-existence of compact spacelike hypersurfaces…
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is…
We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The…
Fully localised three-dimensional solitary waves are steady water waves which are evanescent in every horizontal direction. This paper presents an existence theory for such waves under the assumptions that the relative vorticity and…
We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-waves and the so-called null-cosmologies, we observe an…
We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…
We consider a class of $S^{1}$-bundles whose total space admits a nowhere vanishing recurrent lightlike vector field with respect to a Lorentzian metric. This metric can be modified such that its restricted holonomy group is indecomposable…
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…
We consider generalised pp-waves with purely axial torsion, which we previously showed to be new vacuum solutions of quadratic metric-affine gravity. Our analysis shows that classical pp-waves of parallel Ricci curvature should not be…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
We establish the homogenization results for a class of nonlocal operators of convolution type with integrable jumping kernel $p$ multiplied by rapidly oscillating periodic or locally periodic coefficients. The associated measure $p(z)dz$ is…
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for…
We write the equation of geodesic deviations in the spacetime of $pp$-waves in terms of the Newman-Penrose scalars and apply it to study gravitational waves in quadratic curvature gravity. We show that quadratic curvature gravity $pp$-waves…
In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…
The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney--Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances…
The propagation of finite-amplitude linearly-polarized inhomogeneous transverse plane waves is considered for a Mooney-Rivlin material maintained in a state of finite static homogeneous deformation. It is shown that such waves are possible…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…