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

Nonlinear Sciences – Pattern Formation and Solitons

Scientific paper

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Scientific paper

10.1088/0031-8949/2008/T132/0140

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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