Small-amplitude nonlinear waves on a black hole background

On Nonlinear Water Waves in a Channel

Digging Deeper: Observing Primordial Gravitational Waves below the Binary-Black-Hole-Produced Stochastic Background.

The merger rate of black hole binaries inferred from the detections in the first Advanced LIGO science run implies that a stochastic background produced by a cosmological population of mergers will likely mask the primordial gravitational wave background. Here we demonstrate that the next generation of ground-based detectors, such as the Einstein Telescope and Cosmic Explorer, will be able to o...

On the amplitude equations for weakly nonlinear surface waves

Nonlocal generalizations of Burgers’ equation were derived in earlier work by Hunter [Contemp. Math. 1989], and more recently by Benzoni-Gavage and Rosini [Comput. Math. Appl. 2009], as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage [Diff...

Existence and Blow up of Small-amplitude Nonlinear Waves with a Sign-changing Potential

We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of smallamplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time.

Perturbations in the Kerr-Newman Dilatonic Black Hole Background: Maxwell Waves, the Dilaton Background and Gravitational Lensing

In this paper we continue the analysis of one of our previous papers and study the affect of the existence of a non-trivial dilaton background on the propagation of electromagnetic waves in the Kerr-Newman dilatonic black hole space-time. For this purpose we again employ the double expansion in both the background electric charge and the wave parameters of the relevant quantities in the Newman-...