Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation

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dc.creatorBrusch, Lutz
dc.creatorTorcini, Alessandro
dc.creatorvan Hecke, Martin
dc.creatorZimmermann, Martin G.
dc.creatorBaer, Markus
dc.date2001-04-10
dc.date.accessioned2026-07-07T05:33:25Z
dc.date.available2026-07-07T05:33:25Z
dc.descriptionThe transition from phase chaos to defect chaos in the complex Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown to be limited by a maximum P_SN which depends on the CGLE coefficients; MAW-like structures with period larger than P_SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients $ν\approx 0$ and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings p between neighboring peaks of the phase gradient. A systematic comparison of p and P_SN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than P_SN. In other words, MAWs with period P_SN represent ``critical nuclei'' for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time. We conjecture that in the regime where the maximum period P_SN has diverged, phase chaos persists in the thermodynamic limit.
dc.description25 pages, 18 figures
dc.identifierhttps://arxiv.org/abs/nlin/0104029
dc.identifierhttp://arxiv.org/abs/nlin/0104029
dc.identifierPhysica D 160, 127 (2001)
dc.identifierdoi:10.1016/S0167-2789(01)00355-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79989
dc.subjectChaotic Dynamics
dc.subjectDisordered Systems and Neural Networks
dc.subjectDynamical Systems
dc.subjectPattern Formation and Solitons
dc.subjectFluid Dynamics
dc.titleModulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
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