Onset of Chaos in the Generalized Ginzburg-Landau Equation

  • Boris A. Malomed
  • Alexander A. Nepomnyashchy
Part of the NATO ASI Series book series (NSSB, volume 225)


Study of chaos in the generalized Ginzburg-Landau equation (GLE)
$$ {\text{iu}}_{\text{t}} + {\text{u}}_{{\text{xx}}} + 2\left| {\text{u}} \right|^{\text{2}} {\text{u}} = {\text{i}} \in _1 {\text{u}} - {\text{i}} \in _3 \left| {\text{u}} \right|^2 {\text{u}} + {\text{i}} \in _2 u_{{\text{xx}}} $$
is a subject of great current interest, see, e.g., Refs. 1–6. We will consider Eq. (1) with the periodic boundary condition
$$ {\text{u(x)}} = {\text{u(x}} + 2\pi /{\text{k}}). $$


Modulational Instability Strange Attractor Lorenz System Instability Threshold Lorenz Model 
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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Boris A. Malomed
    • 1
  • Alexander A. Nepomnyashchy
    • 2
  1. 1.P. P. Shirshov Institute for Oceanology of the USSR Academy of SciencesMoscowUSSR
  2. 2.Institute for Continuous Media Mechanics of the Ural Branch of the USSR Academy of SciencesPermUSSR

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