The phase-turbulent (PT) regime for the one-dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient integration scheme. Particular attention is paid to solutions with a nonzero phase gradient. For fixed control parameters, solutions with conserved average phase gradient ν exist only for |ν| less than some upper limit. The transition from phase to defect turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of nonchaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves traveling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a type of quasiperiodic behavior. The main features of these traveling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.

DOI:https://doi.org/10.1103/PhysRevE.55.5073