6 References

6.0.1 Bibliography

1. The world of the complex Ginzburg-Landau equation
   I.S. Aranson and L. Kramer, Rev. Mod. Phys. 74:99-143, 2002
2. Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation
   N. Bekki and K. Nozaki, Phys. Lett. A110:133-135, 1985
3. Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation
   H. Chaté, Nonlinearity 7:185-204, 1994
4. Phase diagram of the two-dimensional complex Ginzburg-Landau equation
   H. Chaté and P. Manneville, Physica A 224:348-368, 1996
5. Stable small-amplitude solutions in reaction-diffusion systems
   G.B. Ermentrout, Quart. Appl. Math. 39:61-86, 1981
6. X-ray scattering by crystals in the neighbourhood of the Curie point
   L.D. Landau, 1937 in collected papers of L.D. Landau (Gordon and Breach, New York)
7. On the problem of turbulence
   L.D. Landau, 1944 in collected papers of L. D. Landau (Gordon and Breach, New York)
8. Traveling hole solutions of the complex Ginzburg-Landau equation: a review
   J. Lega 152-153:269-287, 2001
9. Finite bandwidth, finite amplitude convection
   A.C. Newell and J.A. Whitehead, J. Fluid Mech. 38:279-303, 1969
10. The stability of standing waves with small group velocity
    H. Riecke and L. Kramer, Physica D 137:124-142, 2000
11. Distant side-walls cause slow amplitude modulation of cellular convection
    L.A. Segel, J. Fluid Mech. 38:203-224, 1969
12. On the non-linear mechanics of wave disturbances in stable and unstable parallel flows
    J.T. Stuart, J. Fluid. Mech. 9:353-370 1960
13. Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation
    B.I. Shraiman, A. Pumir, W. van Saarloos, P.C. Hohenberg, H. Chate and M. Holen, Physica D 57:241-248, 1992
14. Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wavesystems
    M. van Hecke, C. Storm and W. van Saarloos, Physica D 134:1-47, 1999
15. Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
    W. van Saarloos, P.C. Hohenberg, Physica D 56:303-367, 1992

6.0.2 Resources

• CGLsim1D.m
  Matlab program that simulates the evolution of the one-dimensional CGL equation using pseudo-spectral code for the derivatives terms and exponential time-stepping for the time integration.

• CGLsim2D.m
  Matlab program that simulates the evolution of the two-dimensional CGL equation using pseudo-spectral code for the derivatives terms and exponential time-stepping for the time integration. Here, a square container is assumed.

6.0.3 Links

• http://www.cmp.caltech.edu/~mcc/STChaos/
  Java simulator (with available source code) for the modified Ginzburg-Landau equation

  

  as well as the Bar-Eiswirth model and coupled quadratic maps.

• http://www.maths.nottingham.ac.uk/personal/pmxdmw/