Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations

We investigate the existence, formation and stability of multipulse bound states in a system of two Ginzburg-Landau equations coupled by linear terms. The system includes linear gain, diffusion, dispersion, and cubic nonlinearity in one component, and only linear losses in the other. This is a straightforward model of a doped dual-core nonlinear optical fiber in which only one core is pumped. The model supports exact stable solitary-pulse solutions. By means of systematic numerical simulations, we find that bound states of two, three, and more pulses with a uniquely determined separation between them exist. The three-pulse bound states are stable against symmetric perturbations, but prove to be unstable against asymmetric ones. Only the two-pulse states are found to be fully stable.