Weakly non-linear dynamics in reaction -- diffusion systems with L\'{e}vy flights
Pattern Formation and Solitons
2009-11-13 v1
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.
Cite
@article{arxiv.0712.4058,
title = {Weakly non-linear dynamics in reaction -- diffusion systems with L\'{e}vy flights},
author = {Y. Nec and A. A. Nepomnyashchy and A. A. Golovin},
journal= {arXiv preprint arXiv:0712.4058},
year = {2009}
}