(1) Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham, UK;(2) Ufa Scientific Center, Institute of Mathematics, RAS, Ufa, Russia;(3) Marconi Solstis, Stratford-Upon-Avon, UK
Abstract:
We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.