Collisions of counter-propagating pulses in coupled complex cubic-quintic Ginzburg–Landau equations

We discuss the results of the interaction of counter-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 cubic cross-coupling, c_r, of the counter-propagating waves as variables while keeping all other parameters fixed. The novel phase diagram in the limit v ↦0, c_r ↦0 turns out to be particularly rich and includes bound pairs of 2 π holes as well as zigzag bound pairs of pulses.