One-dimensional Complex Ginzburg-Landau Equation Research Articles

Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation.

Uniformly translating solutions of the one-dimensional complex Ginzburg-Landau equation are studied near a subcritical bifurcation. Two classes of solutions are singled out since they are often produced starting from localized initial conditions: moving fronts and stationary pulses. A particular exact analytic front solution is found, which is conjectured to control the relative stability of pulses and fronts. Numerical solutions of the Ginzburg-Landau equation confirm the predictions based on this conjecture.

Evolution of the order parameter in situations with broken rotational symmetry

We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.