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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 1, Pages 56–63
DOI: https://doi.org/10.4213/tmf1831
(Mi tmf1831)
 

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

Statistical Approach to Modulational Instability in Nonlinear Discrete Systems

D. Grecu, A. Visinescu

National Institute for Physics and Nuclear Engineering
Full-text PDF (183 kB) Citations (5)
References:
Abstract: We use a statistical approach to investigate the modulational instability (Benjamin–Feir instability) in several nonlinear discrete systems: the discrete nonlinear Schrodinger (NLS) equation, the Ablowitz–Ladik equation, and the discrete deformable NLS equation. We derive a kinetic equation for the two-point correlation function and use a Wigner–Moyal transformation to write it in a mixed space-wave-number representation. We perform a linear stability analysis of the resulting equation and discuss the obtained integral stability condition using several forms of the initial unperturbed spectrum (Lorentzian and $\delta$-spectrum). We compare the results with the continuum limit (the NLS equation) and with previous results.
Keywords: modulational instability – nonlinear discrete systems.
English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 1, Pages 927–934
DOI: https://doi.org/10.1007/s11232-005-0119-5
Bibliographic databases:
Language: Russian
Citation: D. Grecu, A. Visinescu, “Statistical Approach to Modulational Instability in Nonlinear Discrete Systems”, TMF, 144:1 (2005), 56–63; Theoret. and Math. Phys., 144:1 (2005), 927–934
Citation in format AMSBIB
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\paper Statistical Approach to Modulational Instability in Nonlinear Discrete Systems
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\transl
\jour Theoret. and Math. Phys.
\yr 2005
\vol 144
\issue 1
\pages 927--934
\crossref{https://doi.org/10.1007/s11232-005-0119-5}
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Linking options:
  • https://www.mathnet.ru/eng/tmf1831
  • https://doi.org/10.4213/tmf1831
  • https://www.mathnet.ru/eng/tmf/v144/i1/p56
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:328
    Full-text PDF :181
    References:44
    First page:1
     
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