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 li near gain and nonlinear dispersion, or the broadband gain, linear disp ersion, and nonlinear losses. The models have applications in nonlinea r 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 mu lti-pulse array in the latter model is destroyed by the instability ve ry slowly. Considering bound states of two pulses, we conclude that th ey may form a robust bound state in both models. Conditions which allo w for formation of the bound states qualitatively differ in the two mo dels.