Oscillatory instability in super-diffusive reaction diffusion systems: Fractional amplitude and phase diffusion equationsY. 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 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