相关论文: Plane waves with weak singularities
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…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
In this article, we examine the possibility that there exist special scalar-tensor theories of gravity with completely nonsingular FRW solutions. Our investigation in fact shows that while most probes living in such a Universe never see the…
We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to…
Through the AdS/CFT correspondence, Lifshitz spacetimes describe field theories with dynamical scaling ($z \neq 1$). Although curvature invariants are small, the Lifshitz metric exhibits a null singularity in the IR with a large tidal force…
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in a…
Recent developments in string theory have brought forth a considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum…
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…
Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in…
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
We present plane-wave-type solutions of the lowest order superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a stringy generalization of the Brinkmann metric. Some…
We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a…
The presence of fields with negative mass-squared typically leads to some form of instability in standard field theories. The observation that, at least in the light-cone gauge, strings propagating in plane wave spacetimes can have…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…