Movatived by a problem of the dynamical elasticity of crystals with mi
crostructure, a conservative numerical scheme is employed to study the
very long time evolution and interaction of soliton-like solutions in
systems of Coupled Nonlinear Schrodinger Equations. Head-on collision
and overtaking receive special attention. The results obtained demons
trate the inelasticity (change of polarization) of the interaction eve
n for initially circularly polarized components. Thus it may be said t
hat the interactions in such systems break the symmetry of the input.