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Modulational instability and spatiotemporal transition to chaos

Author

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

Abstract

The one-dimensional generalized modified complex Ginzburg–Landau equation [Malomed BA, Stenflo L. J Phys A: Math Gen 1991;24:L1149] is considered. The linear stability analysis is used in order to derive the conditions for modulational instability. We obtained the generalized Lange and Newell’s criterion for modulational instability. Numerical simulation shows the validity of the analytical approach. The model presents a rich variety of patterns propagating in the system and a spatiotemporal transition to chaos.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:914-925
    DOI: 10.1016/j.chaos.2005.04.039
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    Cited by:

    1. Belmonte-Beitia, Juan & Pérez-García, Víctor M. & Vekslerchik, Vadym, 2007. "Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1268-1277.
    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.
    3. Deffo, Guy Roger & Yamgoué, Serge Bruno & Pelap, François Beceau, 2021. "Bifurcation of solitary and periodic waves of an extended cubic-quintic Schrödinger equation with nonlinear dispersion effects governing modulated waves in a bandpass inductor-capacitor network," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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