Self-similar parabolic optical solitary waves

Boscolo, Sonia; Turitsyn, Sergei K.; Novokshenov, V.Yu. and Nijhof, J.H.B. (2002). Self-similar parabolic optical solitary waves. Theoretical and mathematical physics, 133 (3), pp. 1647-1656.

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.

Uncontrolled Keywords: nonlinear optics, generation of parabolic pulses, self-similarity
Published Date: 2002

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