Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation.
We discuss time-dependent spatially localized solutions of the quintic complex Ginzburg-Landau equation applicable near a weakly inverted bifurcation to traveling waves. We find that there are---in addition to the stationary pulses reported previously---stable localized solutions that are periodic, quasiperiodic, or even chaotic in time. An intuitive picture for the stability of these time-dependent localized solutions is presented and the novelty of these phenomena in comparison to localized solutions arising for exactly integrable systems is emphasized.