Stability and interactions of pulses in simplified Ginzburg-Landau equations

We consider in detail two special types of the parameter-free Ginzburg-Landau equation, viz., the ones that combine the bandwidth-limited linear gain and nonlinear dispersion, or the broadband gain, linear dispersion, and nonlinear losses. The models have applications in nonlinear fiber optics and traveling-wave convection. They have exact solitary-pulse solutions which are subject to a background instability. In the former model, we find that the solitary pulse is much more stable than a "densely packed" multi-pulse array. On the contrary to this, a multi-pulse array in the latter model is destroyed by the instability very slowly. Considering bound states of two pulses, we conclude that they may form a robust bound state in both models. Conditions which allow for formation of the bound states qualitatively differ in the two models.