Nonlinear surface plasmons

We derive an asymptotic equation for quasi-static, nonlinear surface plasmons propagating on a planar interface between isotropic media. The plasmons are nondispersive with a constant linearized frequency that is independent of their wavenumber. The spatial profile of a weakly nonlinear plasmon satisfies a nonlocal, cubically nonlinear evolution equation that couples its left-moving and right-moving Fourier components. We prove short-time existence of smooth solutions of the asymptotic equation and describe its Hamiltonian structure. We also prove global existence of weak solutions of a unidirectional reduction of the asymptotic equation. Numerical solutions show that nonlinear effects can lead to the strong spatial focusing of plasmons. Solutions of the unidirectional equation appear to remain smooth when they focus, but it is unclear whether or not focusing can lead to singularity formation in solutions of the bidirectional equation

Sky localization of complete inspiral-merger-ringdown signals for nonspinning massive black hole binaries

We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\times10^6 M\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic telescopes, such as the James Webb Space Telescope, that could be used to search for electromagnetic signals associated with merging massive black holes. We investigate the way in which parameter errors decrease with measurement time, focusing specifically on the additional information provided during the merger-ringdown segment of the signal. We find that this information improves all parameter estimates directly, rather than through diminishing correlations with any subset of well- determined parameters. Although we have employed the baseline LISA design for this study, many of our conclusions regarding the information provided by mergers will be applicable to alternative mission designs as well.Comment: 9 pages, 5 figures, submitted to Phys. Rev.