Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials

摘要

Two analytical techniques for the generation of wide classes of exact solutions of the nonlinear Schrödingerudequation (NLSE) containing an external potential areudproposed. Both methods are illustrated by a variety ofudlocalized solutions, including solitary optical vortices, for both the self-focusing and self-defocusing nonlinearities. The stability of solutions was tested by direct numerical simulations of the NLSE; the existence of stable localized modes was confirmed through the simulation.