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TMF, 1986, Volume 69, Number 1, Pages 40–54 (Mi tmf5202)  

This article is cited in 5 scientific papers (total in 5 papers)

Complete asymptotic representation of an electromagnetic pulse in a long two-level amplifier

S. V. Manakov, V. Yu. Novokshenov


Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1986, 69:1, 987–997

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Received: 03.07.1985

Citation: S. V. Manakov, V. Yu. Novokshenov, “Complete asymptotic representation of an electromagnetic pulse in a long two-level amplifier”, TMF, 69:1 (1986), 40–54; Theoret. and Math. Phys., 69:1 (1986), 987–997

Citation in format AMSBIB
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\by S.~V.~Manakov, V.~Yu.~Novokshenov
\paper Complete asymptotic representation of an~electromagnetic pulse in a~long two-level amplifier
\jour TMF
\yr 1986
\vol 69
\issue 1
\pages 40--54
\mathnet{http://mi.mathnet.ru/tmf5202}
\zmath{https://zbmath.org/?q=an:0625.35070}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 69
\issue 1
\pages 987--997
\crossref{https://doi.org/10.1007/BF01037673}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986H110300003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. T. Habibullin, “Integrable initial-boundary-value problems”, Theoret. and Math. Phys., 86:1 (1991), 28–36  mathnet  crossref  mathscinet  zmath  isi
    2. Quantum Electron., 40:9 (2010), 756–781  mathnet  crossref  adsnasa  isi  elib
    3. V. P. Kotlyarov, E. A. Moskovchenko, “Matrix Riemann–Hilbert Problems and Maxwell–Bloch Equations without Spectral Broadening”, Zhurn. matem. fiz., anal., geom., 10:3 (2014), 328–349  mathnet  crossref  mathscinet
    4. M. S. Filipkovska, V. P. Kotlyarov, E. A. Melamedova (Moskovchenko), “Maxwell–Bloch equations without spectral broadening: gauge equivalence, transformation operators and matrix Riemann–Hilbert problems”, Zhurn. matem. fiz., anal., geom., 13:2 (2017), 119–153  mathnet  crossref
    5. Vladimir P. Kotlyarov, “A Matrix Baker–Akhiezer Function Associated with the Maxwell–Bloch Equations and their Finite-Gap Solutions”, SIGMA, 14 (2018), 082, 27 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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