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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf1831https://doi.org/10.4213/tmf1831 https://www.mathnet.ru/eng/tmf/v144/i1/p56
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Abstract page: | 328 | Full-text PDF : | 181 | References: | 44 | First page: | 1 |
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