The generation of stable dense soliton trains in passively mode-locked ring
fiber lasers was explored theoretically. We found equilibrium states of ev
en and odd numbers of interacting solitons in a ring configuration by emplo
ying soliton perturbation theory. In a lossless ring, these equilibrium sta
tes were unstable due to the lack of a damping mechanism both for the oscil
lations in the solitons parameters as well as for modulation instability. I
n a passively mode-locked ring fiber laser, these dense soliton trains were
self-stabilized to form ordered trains. The stabilization process was init
iated by the local repulsive soliton-soliton interactions and preceeded by
a global soliton phase locking stemming from multimode self-injection locki
ng. We describe in detail the evolution from a disordered to ordered dense
soliton train.