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arXiv · 0712.4058

Weakly non-linear dynamics in reaction -- diffusion systems with Lévy flights

Y. Nec·A. A. Nepomnyashchy·A. A. Golovin
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Abstract

Reaction--diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties of the normal complex Ginzburg-Landau equation are generalised for the fractional analogue. In particular, an analogue of Kuramoto-Sivashinsky equation is derived.

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Y. Nec, A. A. Nepomnyashchy, A. A. Golovin. 2007-12-25. Weakly non-linear dynamics in reaction -- diffusion systems with Lévy flights. https://doi.org/10.1088/0031-8949/2008/t132/014043

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