Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation

Details Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation

2001-04-27

arxiv.org/abs/nlin/0104067v1

Nonlinear Sciences

Pattern Formation and Solitons

20 pages, 11 figures

Scientific paper

10.1016/S0167-2789(01)00348-7

We study the dynamics of the one-dimensional complex Ginzburg Landau equation (CGLE) in the regime where holes and defects organize themselves into composite superstructures which we call zigzags. Extensive numerical simulations of the CGLE reveal a wide range of dynamical zigzag behavior which we summarize in a `phase diagram'. We have performed a numerical linear stability and bifurcation analysis of regular zigzag structures which reveals that traveling zigzags bifurcate from stationary zigzags via a pitchfork bifurcation. This bifurcation changes from supercritical (forward) to subcritical (backward) as a function of the CGLE coefficients, and we show the relevance of this for the `phase diagram'. Our findings indicate that in the zigzag parameter regime of the CGLE, the transition between defect-rich and defect-poor states is governed by bifurcations of the zigzag structures.

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