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Pattern selection and modulational instability in the one-dimensional modified complex Ginzburg–Landau equation

Author

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  • Mohamadou, Alidou
  • Jiotsa, A. Kenfack
  • Kofané, T.C.

Abstract

We study analytically modulational instability in the one-dimensional modified complex Ginzburg–Landau equation for the travelling wave systems. The linear stability analysis is used to get domains of instability. We derive the Lange and Newell’s criterion for modulational instability. Moreover, it is shown that a modulationally unstable pattern is selected and propagates into an initially unstable motionless state in the system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:4:p:957-966
    DOI: 10.1016/j.chaos.2004.09.106
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    Cited by:

    1. Zhang, Qi, 2009. "Random attractors for a Ginzburg–Landau equation with additive noise," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 463-472.
    2. 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.

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