Volume 82, Number 5, June 2008
Article Number 58003
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 27 May 2008
EPL, 82 (2008) 58003
DOI: 10.1209/0295-5075/82/58003

Oscillatory instability in super-diffusive reaction $\hbox{--}$ diffusion systems: Fractional amplitude and phase diffusion equations

Y. Nec1, A. A. Nepomnyashchy1 and A. A. Golovin2

1  Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel
2  Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL USA

received 10 February 2008; accepted in final form 12 April 2008; published June 2008
published online 27 May 2008

Non-linear evolution of a reaction $\hbox{--}$ super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of the complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical solutions are studied.

82.40.Ck - Pattern formation in reactions with diffusion, flow and heat transfer.

© EPLA 2008