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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)
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DOI: https://doi.org/10.4213/tmf1831
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 δ-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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\by D.~Grecu, A.~Visinescu
\paper Statistical Approach to Modulational Instability in Nonlinear Discrete Systems
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\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:
    1. Grecu D., Carstea A.S., Grecu A.T., Visinescu A., “Statistical Approach of Modulation Instability in the Class of NLS Equations”, Rom. J. Phys., 61:1-2 (2016), 124–134  isi  elib
    2. Visinescu A., Grecu D., “Statistical Approach of Modulational Instability Beyond Gaussian Approximation”, Xxth International Conference on Integrable Systems and Quantum Symmetries (Isqs-20), Journal of Physics Conference Series, 411, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013, 012029  crossref  isi  scopus
    3. Grecu, AT, “Statistical Approach of Modulational Instability in Cylindrical/Spherical NLS Equation”, Romanian Reports in Physics, 61:3 (2009), 467  isi
    4. Grecu A.T., De Nicola S., Fedele R., Grecu D., Visinescu A., “Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach”, 7th International Conference of the Balkan Physical Union, AIP Conference Proceedings, 1203, 2009, 1239–1244  isi
    5. Grecu AT, Grecu D, Visinescu A, “Statistical approach of modulational instability in the class of derivative nonlinear Schrodinger equations”, International Journal of Theoretical Physics, 46:5 (2007), 1190–1204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    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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