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The Complex Ginzburg-Landau equation II (also real case)

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. Simulations!. Simulations!. I. Aronson, L. Aronson, LK, A. Weber PRA 1992).

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The Complex Ginzburg-Landau equation II (also real case)

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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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