Related papers: Towards a classification of wave catastrophes
In a two-dimensional microwave chaotic cavity ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous…
We consider the conditions under which solitary waves can exist in elongated clouds of Bose-Einstein condensed atoms. General expressions are derived for the velocity, characteristic size, and spatial profile of solitary waves, and the low-…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a…
We consider the Cauchy problem for the wave equation in a general class of spherically symmetric black hole geometries. Under certain mild conditions on the far-field decay and the singularity, we show that there is a unique globally smooth…
We introduce a family of solutions of Einstein's gravity minimally coupled to an anisotropic fluid, describing asymptotically flat black holes with "hair" and a regular horizon. These spacetimes can describe the geometry of galaxies…
Inertial waves in convective regions of stars exhibit topological properties linked to a Chern number of 1. The first of these is a unique, unidirectional, prograde oscillation mode within the cavity, which propagates at arbitrarily low…
This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…
In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of…
We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties…
We simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we find that a horizon…
It is demonstrated that static, charged, spherically--symmetric black holes in string theory are classically and catastrophically unstable to linearized perturbations in four dimensions, and moreover that unstable modes appear for…
The group velocity of gravitational waves in a flat Friedman-Robertson-Walker universe is investigated. For plane waves with wavelength well inside the horizon, and a universe filled with an ideal fluid with the pressure to density ratio…
Gravitons radiated from light, evaporating black holes contribute to the stochastic background of gravitational waves. The spectrum of such emission depends on both the mass and the spin of the black holes, as well as on the redshifting…
Power induced wave collapse is one of the most fascinating phenomena in optics as it provides extremely high intensities, thus stimulating a range of nonlinear processes. For low power levels, propagation of beams in bulk media is dominated…
Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and…
Extremal six-dimensional black string solutions with some non-trivial momentum distribution along the wave are considered. These solutions were recently shown to contain a singularity at the would-be position of the event horizon. In the…
We use a third-order perturbation theory and Melnikov's method to prove the existence of chaos in spinning circular disks subject to a lateral point load. We show that the emergence of transverse homoclinic and heteroclinic points…
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to…
We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting…