Complete asymptotic representation of an electromagnetic pulse in a long two-level amplifier
type: Item
instance of: scholarly article
title: Complete asymptotic representation of an electromagnetic pulse in a long two-level amplifier
zbMATH Open document ID: 0625.35070
DOI: 10.1007/BF01037673
author: S. V. Manakov
author: V. Yu. Novokshenov
published in: Theoretical and Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 4015315
zbMATH Keywords: electromagnetic wave
zbMATH Keywords: nonlinear two-level medium
zbMATH Keywords: Lamb's semiclassical theory
zbMATH Keywords: Maxwell-Bloch equations
zbMATH Keywords: inverse scattering method
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Painlevé equation
zbMATH Keywords: rapidly oscillating self-similar regime
zbMATH Keywords: scattering data
MaRDI profile type: Publication
cites work: Q3913845
cites work: Monodromy- and spectrum-preserving deformations. I
cites work: Q5682682
description: scientific article; zbMATH DE number 4015315