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Kvantovaya Elektronika, 2007, Volume 37, Number 6, Pages 561–564 (Mi qe13494)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear optical phenomena

Complex periodic solutions of the nonlinear Schrödinger equation and nondegenerate multicomponent cnoidal waves in parametric frequency conversion

V. M. Petnikova, V. V. Shuvalov

International Laser Center of Moscow State University

Abstract: A new type of complex periodic solutions of the nonlinear Schrödinger equation is described which can be obtained in the collinear interaction of three plane monochromatic waves (modes) in a quadratic nonlinear medium. On passing to real variables (quadrature components), the solutions of this new type describe nondegenerate two-component cnoidal waves consisting of two 'incoherent' (noninterfering) components. The amplitudes of these components perform additional (with respect to the modulus oscillations) intricate nonlinear oscillations phase-shifted by π/2, which are consistent with oscillations of the solution modulus described by an elliptic function.

Full text: PDF file (125 kB)

English version:
Quantum Electronics, 2007, 37:6, 561–564

Bibliographic databases:

PACS: 42.65.Ky, 42.65.Yj, 42.65.Tg, 05.45.-a
Received: 12.12.2006

Citation: V. M. Petnikova, V. V. Shuvalov, “Complex periodic solutions of the nonlinear Schrödinger equation and nondegenerate multicomponent cnoidal waves in parametric frequency conversion”, Kvantovaya Elektronika, 37:6 (2007), 561–564 [Quantum Electron., 37:6 (2007), 561–564]

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  • http://mi.mathnet.ru/eng/qe13494
  • http://mi.mathnet.ru/eng/qe/v37/i6/p561

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Quantum Electron., 40:3 (2010), 219–222  mathnet  crossref  adsnasa  isi  elib
    2. Quantum Electron., 40:7 (2010), 619–623  mathnet  crossref  adsnasa  isi  elib
    3. Quantum Electron., 42:12 (2012), 1118–1122  mathnet  crossref  adsnasa  isi  elib
  • Квантовая электроника Quantum Electronics
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