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Movatived by a problem of the dynamical elasticity of crystals with microstructure, 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 demonstrate the inelasticity (change of polarization) of the interaction even for initially cir- cularly polarized components. Thus it may be said that thedoi:10.1088/0031-8949/50/5/001 fatcat:l6xypos5bvbfpgdparvu5sihae