  The asymptotic regimes of the N-site complex Toda chain (CTC) with fixed ends
related to the classical series of simple Lie algebras are classified. It is
shown that the CTC models have much richer variety of asymptotic regimes than
the real Toda chain (RTC). Besides asymptotically free propagation (the only
possible regime for the RTC), CTC allow bound state regimes, various
intermediate regimes when one (or several) group(s) of particles form bound
state(s), singular and degenerate solutions. These results can be used e.g., in
describing the soliton interactions of the nonlinear Schroedinger equation.
Explicit expressions for the solutions in terms of minimal sets of scattering
data are proposed for all classical series B_r - D_r.
