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Modulational instability in linearly coupled complex cubic–quintic Ginzburg–Landau equations

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  • Porsezian, K.
  • Murali, R.
  • Malomed, Boris A.
  • Ganapathy, R.

Abstract

We investigated the modulational instability (MI) of symmetric and asymmetric continuous-wave (CW) solutions in a model of a laser based on a dual-core nonlinear optical fiber. The model is based on a pair of linearly coupled cubic–quintic (CQ) complex Ginzburg–Landau (CGL) equations, that were recently shown to support several types of symmetric and asymmetric solitary pulses. We produce characteristics of the MI in the form of typical dependences of the instability growth rate (gain) on the perturbation frequency and system’s parameters. In particular, the gain strongly depends on the spectral-filtering parameter and the CW amplitude itself. Generic outcomes of the nonlinear development of the MI are investigated by dint of direct simulations of the underlying equations. Three typical outcomes are found: a periodic chain of localized growing peaks; a stable array of stationary pulses (which is a new type of a stationary state in the model), and an apparently turbulent state.

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  • Porsezian, K. & Murali, R. & Malomed, Boris A. & Ganapathy, R., 2009. "Modulational instability in linearly coupled complex cubic–quintic Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1907-1913.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1907-1913
    DOI: 10.1016/j.chaos.2007.09.086
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    References listed on IDEAS

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    1. Mancas, Stefan & Choudhury, S. Roy, 2006. "Bifurcations and competing coherent structures in the cubic-quintic Ginzburg–Landau equation I: Plane wave (CW) solutions," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1256-1271.
    2. Mohamadou, Alidou & Jiotsa, A. Kenfack & Kofané, T.C., 2005. "Pattern selection and modulational instability in the one-dimensional modified complex Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 957-966.
    3. Zhang, Jin-Liang & Wang, Ming-Liang & Gao, Ke-Quan, 2007. "Exact solutions of generalized Zakharov and Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1877-1886.
    4. Mohamadou, Alidou & Kenfack-Jiotsa, A. & Kofané, T.C., 2006. "Modulational instability and spatiotemporal transition to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 914-925.
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    Cited by:

    1. Kumar, Vineesh & Patel, Arvind, 2020. "Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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