Hamburg 2001 – scientific programme
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DY: Dynamik und Statistische Physik
DY 12: Strukturbildung und Turbulenz II
DY 12.6: Talk
Monday, March 26, 2001, 12:15–12:30, S 5.5
Fully Nonlinear Analysis of the Eckhaus Instability: Superspirals and Spiral Breakup — •Lutz Brusch1, Alessandro Torcini2, and Markus Bär1 — 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden — 2Dipartimento di Fisica, Universita’ “La Sapienza”, P.le A. Moro 2, I-00185 Roma, Italy
The Eckhaus instability of traveling waves in the complex
Ginzburg-Landau equation (CGLE) produces modulated amplitude waves
(MAWs) that are parametrized by the spatial period of the modulation
and the average local wave number (winding number).
Using continuation software
(AUTO97), we analyzed existence and stability of these MAWs.
They bifurcate supercritically (subcritically) for small (large)
wavenumber near the Eckhaus instability and disappear in a saddle-node
bifurcation. These observations offer a consistent interpretation of
recent experiments, that exhibit a transition from rotating spirals to
modulated ,,superspirals” and finally to spiral breakup in a pattern
forming chemical reaction (1) and extend earlier work on MAWs
with zero winding number (2).
(1) L. Q. Zhou and Q. Ouyang, Phys. Rev. Lett. 85, 1600 (2000)
(2) L. Brusch et al., Phys. Rev. Lett. 85, 86 (2000)