Secondary structures in a one-dimensional complex Ginzburg-Landau equation with homogeneous boundary conditions

Experiments in extended systems, such as the counter-rotating Couette-Taylor flow or the Taylor-Dean flow system, have shown that patterns with vanishing amplitude may exhibit periodic spatio-temporal defects for some range of control parameters. These observations could not be interpreted by the complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. We have investigated the one-dimensional CGLE with homogeneous boundary conditions. We found that, in the 'Benjamin-Feir stable' region, the basic wave train bifurcates to state with periodic spatio-temporal defects. The numerical results match the observations quite well. We have built a new state diagram in the parameter plane spanned by the criticality (or equivalently the linear group velocity) and the nonlinear frequency detuning.