  We analyze the dynamical behavior of the $N$-soliton train in the adiabatic
approximation of the Manakov model. %perturbed by gain/loss effects and also by
several types of external potentials. The evolution of Manakov $N$-soliton
trains is described by the complex Toda chain (CTC) which is a completely
integrable dynamical model. Calculating the eigenvalues of its Lax matrix
allows us to determine the asymptotic velocity of each soliton. So we describe
sets of soliton parameters that ensure one of the two main types of asymptotic
regimes: the bound state regime (BSR) and the free asymptotic regime (FAR). In
particular we find explicit description of special symmetric configurations of
$N$ solitons that ensure BSR and FAR. We find excellent matches between the
trajectories of the solitons predicted by CTC with the ones calculated
numerically from the Manakov system for wide classes of soliton parameters.
This confirms the validity of our model.
