Abstract

We discuss the results of the interaction ofcounter-propagating pulses for two coupled complex cubic-quintic Ginzburg-Landau equations as they arise near the onset of a weakly inverted Hopf bifurcation. As a result of the interaction of the pulses we find in 1D for periodic boundary conditions (corresponding to an annular geometry) many different possible outcomes. These are summarized in two phase diagrams using the approach velocity, v, and the real part of the cubiccross-coupling, c r, of the counter-propagating waves asvariables while keeping all other parameters fixed. The novelphase diagram in the limit v → 0, c r → 0 turns out to beparticularly rich and includes bound pairs of 2 π holes aswell as zigzag bound pairs of pulses. © EDP Sciences/Societé Italiana di Fisica/ Springer-Verlag 2007.