Geodesic
Self-Similar Parabolic Optical Solitary Waves
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 386-397 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: nonlinear optics, self-similarity, generation of parabolic pulses. 
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S. Boscolo; S. K. Turitsyn; V. Yu. Novokshenov; J. Nijhof. Self-Similar Parabolic Optical Solitary Waves. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 386-397. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a4/

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