Emergent soliton-like solutions in the parametrically driven 1-D nonlinear Schrödinger equation

Abstract

We numerically investigate the long time dynamics of spatially periodic breather solutions of the 1-D nonlinear Schrödinger equation under parametric forcing of the form $f(x)=f_0\exp (iKx)$ along with dissipation. In the absence of dissipation, robust soliton-like excitations are observed that travel with constant amplitude and velocity. With dissipation, these solitons lose energy (and amplitude) yet gain speed - a characteristic not observed in an ordinary soliton. Moreover, these novel solitons are found to be stable against random perturbations.

12 pages, 8 figures