1 / 23

Fronts in the cubic and quintic complex Ginzburg-Landau equation

Fronts in the cubic and quintic complex Ginzburg-Landau equation. Benasque, September 2003. - Linear fronts in the supercritical case (cubic CGLe) - Normal and retracting fronts in subcritical bifurcations (quintic CGL2) - Spatiotemporal intermittency

derek-cohen
Télécharger la présentation

Fronts in the cubic and quintic complex Ginzburg-Landau equation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fronts in the cubic and quintic complex Ginzburg-Landau equation Benasque, September 2003 - Linear fronts in the supercritical case (cubic CGLe) - Normal and retracting fronts in subcritical bifurcations (quintic CGL2) - Spatiotemporal intermittency - Localized states: pulses and holes - Retracting fronts in supercritical Hopf bifurcations - Collapse (finite-time blow up) - Conclusions Work on retracting fronts together with P. Coullet (Chaos, submitted)

  2. Have allowed For moving frame Amplitude- unstable solutions

  3. The “Front ODE”

  4. The “Front ODEs” (actuallly for all coherent states) Simulation with:

  5. c2=c3=2, ß=0.4 µ=0.1 µ=0.2

  6. as in real case generates phase gradient Actually very old: Hocking and Stewartson 1972 (prevention of blow up)

  7. No collapse for suffiently large | | and not too large b, because of phase gradient effect - 3 S. Popp O. Stiller, E. Kuznetsov LK 1998

  8. c3=15, Initial conditions: small white noise b3=1.5 b3=3 b3=0 b3=-2

  9. Concluding Remarks Retracting Fronts and their consequences are a very general and robust phenomenon (other models, far away from threshold!). Only need nonlinear dispersion. Have various important consequences: - basic state absolutely stable for negative m - spatiotemporal intemittency for positive m (no hysteresis in the subcritical case) - localized structures (pulses and holes) - prevention of blow-up: for subcritical bifurcations the relevant solutions may bifurcate supercritically

More Related