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Fractional Ginzburg-Landau Equation

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Fractional Dynamics

Part of the book series: Nonlinear Physical Science ((NPS,volume 0))

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Abstract

Complex Ginzburg-Landau equation (Aranson and Kramer, 2002) is one of the most-studied equations in physics. This equation describes a lot of phenomena including nonlinear waves, second-order phase transitions, and superconductivity. We note that the Ginzburg-Landau equation can be used to describe the evolution of amplitudes of unstable modes for any process exhibiting a Hopf bifurcation. The equation can be considered as a general normal form for a large class of bifurcations and nonlinear wave phenomena in continuous media systems. The complex Ginzburg-Landau equation is used to describe synchronization and collective oscillation in complex media.

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Tarasov, V.E. (2010). Fractional Ginzburg-Landau Equation. In: Fractional Dynamics. Nonlinear Physical Science, vol 0. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14003-7_9

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