Geodesic
Self-Similar Parabolic Optical Solitary Waves
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 386-397

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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. 
@article{TMF_2002_133_3_a4,
     author = {S. Boscolo and S. K. Turitsyn and V. Yu. Novokshenov and J. Nijhof},
     title = {Self-Similar {Parabolic} {Optical} {Solitary} {Waves}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {386--397},
     publisher = {mathdoc},
     volume = {133},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a4/}
}
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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/