  We numerically investigate the formation of soliton pairs (bound states) in
mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic
Ginzburg-Landau equation) we observe a discrete family of soliton pairs with
equidistantly increasing peak separation. This family was identified by two
alternative numerical schemes and the bound state instability was disclosed by
a linear stability analysis. Moreover, similar families of unstable bound state
solutions have been found in a more realistic lumped laser model with an
idealized saturable absorber (instantaneous response). We show that a
stabilization of these bound states can be achieved when the finite relaxation
time of the saturable absorber is taken into account. The domain of stability
can be controlled by varying this relaxation time.
