Dynamical models of adiabatic $N $-soliton interactions

The adiabatic N-soliton train interactions for the scalar nonlinear Schrodinger (NLS) equation and its perturbed versions are well studied. Here we briefly outline how they can be generalized for the higher NLS-type equations and for the multicomponent NLS equations. It is shown that in all these cases the complex Toda chain plays fundamental role.