Related papers: Comments on the radial plane waves
We give a higher even dimensional extension of vacuum colliding gravitational plane waves with the combinations of collinear and non-collinear polarized four-dimensional metric. The singularity structure of space-time depends on the…
The optimal lifespan estimates of a solution to weakly coupled systems of wave equations have been investigated by many works, except for the lower bound in even space dimensions. Our aim is to prove the open part under the assumption of…
High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be…
The computation of anomalies in quantum field theory may be carried out by evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation of these Jacobians can be cast in the form of a quantum mechanical problem, whose…
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…
PP-waves have recently been of interest to string theorists. This is the original, hard to find, original article on plane polarized gravitational waves.
We construct a bounded plane domain which is Bergman complete but for which the Bergman kernel does not tend to infinity as the point approaches the boundary.
Complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluid. Resonance three-wave interaction processes -- decay instability and confluence of two waves -- are shown to play a key role in the weakly…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.
Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds. A simple example of a plane wave is examined in detail and…
This work starts from the premise that sinusoidal plane waves cease to be solutions of field theories when turning on an interaction. A nonlinear interaction term generates harmonics analogous to those observed in nonlinear optical media.…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…
A new analytical approach to description of electromagnetic waves in nonmagnetic anisotropic media is presented. Amplitudes of their reflection and refraction at interfaces and also reflection and transmission of plane parallel plates are…
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 theoretical description of a class of unidirectional axisymmetric localized pulses, is given. The equivalence of their representations in the form of relatively undistorted quasi-spherical waves, in the form of Fourier-Bessel integrals…
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their…
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative…
Undulatory field functions represent a real wave only if there exists a class of infinite reference systems for which an identical wave is described by the same functional forms.