User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse




Journal Article

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


Ipsen,  Mads
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available

Ipsen, M., & van Hecke, M. (2001). Composite “zigzag” structures in the 1D complex Ginzburg-Landau equation. Physica D, 160(1-2), 103-115. doi:10.1016/S0167-2789(01)00348-7.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0011-172D-8
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.