arXiv subjects

Y. Nec

Publications and source records attributed to Y. Nec.

2 recordsLinked to original sources

arXiv2007

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

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.

nlin.PS↗

arXiv2007

Oscillatory instability in super-diffusive reaction -- diffusion systems: fractional amplitude and phase diffusion equations

Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical solutions are studied.

nlin.PS↗