Geodesic
Complete asymptotic representation of an~electromagnetic pulse in a~long two-level amplifier
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 1, pp. 40-54

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The propagation of an electromagnetic wave in a nonlinear two-level medium described in the framework of Lamb's semiclassical theory is considered. The corresponding system of Maxwell-Bloch equations is investigated by the inverse scattering method with a view to constructing a complete asymptotic expansion of its solutions at large separation from the edge of the region. In the neighborhood of the wave front, the solution is described by a Painlevé equation, whereas far from the front the solution goes over to a rapidly oscillating self-similar regime. In the intermediate region, the parameters of these asymptotic solutions are matched by comparing the corresponding scattering data. 
@article{TMF_1986_69_1_a2,
     author = {S. V. Manakov and V. Yu. Novokshenov},
     title = {Complete asymptotic representation of an~electromagnetic pulse in a~long two-level amplifier},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {40--54},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_69_1_a2/}
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S. V. Manakov; V. Yu. Novokshenov. Complete asymptotic representation of an~electromagnetic pulse in a~long two-level amplifier. Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 1, pp. 40-54. http://geodesic.mathdoc.fr/item/TMF_1986_69_1_a2/