Semi-analytical solutions for dispersive shock waves in colloidal media

Abstract

The diffractive resolution of a discontinuity at the edge of an optical beam in a colloidal suspension of spherical dielectric nanoparticles by a collisionless shock, or dispersive shock wave, is studied. The interaction of the nanoparticles is modelled as a hard-sphere gas with the Carnahan-Starling formula used for the gas compressibility. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. It is found that the discontinuity is resolved through the formation of a dispersive shock wave which forms before the eventual onset of modulational instability. A semi-analytical solution is developed in the (1 + 1) dimensional case by approximating ..