相关论文: Plane waves with weak singularities

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can…

A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This…

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…

We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…

Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…

We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the…

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and find there are two cases to consider; what we call non-exceptional and exceptional. In…

This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…

A strong-weak coupling duality symmetry of the string equations of motion has been suggested in the literature. This symmetry implies that vacua occur in pairs. Since the coupling constant is a dynamical variable in string theory, tunneling…

The metric for gravitational plane waves has very high symmetry (two spacelike commuting Killing vectors). For this high symmetry, a simple renormalization of the lapse function is found which allows the constraint algebra for canonical…

We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…

For a special time-dependent homogeneous plane wave background that includes a null singularity we construct the closed string propagators. We carry out the summation over the oscillator modes and extract the worldsheet spacetime structures…

String theory in an exact plane wave background is explored. A new example of singularity in the sense of string theory for nonsingular spacetime metric is presented. The 4-tachyon scattering amplitude is constructed. The spectrum of states…

Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence: the mutual…

We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow…

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein…

The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…

Electromagnetic waves propagating in the background provided by a spacetime hosting a strong curvature, naked singularity, are fully studied. The analysis is performed not only in the realm of geometrical optics -- which, not surprisingly,…

We investigate the instabilities of low winding number electroweak strings using standard numerical techniques of linear algebra. For strings of unit winding we are able to confirm and extend existing calculations of the unstable region in…