One World Waves S Baqer
From OLLIE Quinn on July 30th, 2020
Title:Dispersive hydrodynamics in a nonlocal nonlinear medium
Abstract:Dispersive shock waves (DSWs), or sometimes known as undular bores in fluid mechanics, are nonlinear dispersive wave phenomena that get generated when physical quantities undergo rapid variations in media whose dispersion dominates viscosity. In this talk, we will present various resonant optical DSW regimes arising in a nonlocal nonlinear medium so-called defocusing nematic liquid crystal. These DSW regimes are generated from discontinuous initial conditions for the optical field and are resonant in that linear dispersive waves are in resonance with the DSW, resulting in a resonant radiation propagating ahead of the DSW itself. Previous studies have used the classical KdV equation and gas dynamic shock wave theory to treat nematic DSWs, but poor agreements with numerical solutions were found. Indeed, the standard DSW structure disappears and a Whitham shock emerges as the initial jumps become sufficiently large. Asymptotic theory, approximate methods or Whitham’s modulation theory are used to find solutions for these resonant nematic DSWs. The comparisons between theoretical and numerical solutions are found excellent in all nematic dispersive hydrodynamic regimes. This is a collaboration project with Noel F. Smyth.