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The Complex Ginzburg-Landau Equation: Insights on Amplitude-Phase Representation

Delve into the dynamics and stability of plane waves, BFN instability, and chaos phenomena in the one-dimensional Real Gle system. Explore simulations and phase diagrams for 1D CGLe, including phase chaos and beyond, such as amplitude chaos and defect chaos. Discover the complexities of spiral-filament chaos in three dimensions. Detailed insights are provided on various instabilities, interactions, and turbulence limits in different dimensions.

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The Complex Ginzburg-Landau Equation: Insights on Amplitude-Phase Representation

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  1. The Complex Ginzburg-Landau equation II (also real case) Amplitude-Phase representation Real Gle (mostly 1D) Stability of plane waves, BFN instability Phase equation Phase and amplitude chaos

  2. Simulations!

  3. Simulations!

  4. I. Aronson, L. Aronson, LK, A. Weber PRA 1992)

  5. Phase diagram for 1D CGLe (b= ) N A I= Absolute stability boundary

  6. Simulations of phase Chaos in 1D H. Chate, 1994

  7. Beyond phase chaos (and coexistenct): “amplitude chaos” (or defect chaos) 1D: nonzero rate of “phase slips” (A=0 at some x,t) 2D: nonzero density of zeros of A (topological point defects) 3D: further restrictions for persistent defect lines

  8. EI = conv. instab., AI=abs. Instab., BFN= Benjamin-Feir-Newell line, OR=monotonic/oscillatory interaction (bound states). L=limit of phase turbulence, T-limit of defect turbulence (Chate & Manneville, 1996)

  9. Spiral-filament chaos in 3D Snapshots at different times =50, c=-0.5 Aranson, Bishop, LK (1998) For more details: Aronson & LK, Rev. Mod. Phys. 74, 99 (2002)

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