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The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial

The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial. Introduction 0D: The Hopf bifurcation (textbooks!) Spatially extended systems, predominantly (standard!) General discussion: wave number band (phase waves) etc.

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The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial

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  1. The Complex Ginzburg Landau equation (CGLe) Mostly a Tutorial Introduction 0D: The Hopf bifurcation (textbooks!) Spatially extended systems, predominantly (standard!) General discussion: wave number band (phase waves) etc. Solutions in 1D: coherent structures (localised states, fronts, Retracting Fronts, phase chaos and defect chaos…) 6. Solutions in 2D (and maybe 3D) vortices and spirals, chaos… What would Landau have said? Pathological ?

  2. u u v Poincare considered the problem too trivial to write down…. Andronov & Leontovich did it in the plane ( ~1938). Hopf generalized it to many dergrees of freedom(1942). The Hopf Bifurcation. In the plane: Ha-ha-ha! v

  3. Re (A) u Actually a structure for Snapshot!

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