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We investigate numerically by a conservative difference scheme in complexarithmetic the head-on and takeover collision dynamics of the solitary waves assolutions of linearly Coupled Nonlinear Schr\"odinger Equations for variousinitial phases. The initial conditions are superposition of two one-solitonsolutions with general polarization. The quasi-particle behavior of propagatingand interacting solutions in conditions of rotational polarization is examined.We find that the total mass, pseudomomentum and energy are conserved while thelocal masses, individual and total polarization depend strongly on the linearcoupling and the initial phase difference. We also find out that thepolarization angle of the quasi-particles can change independently of theinteraction.

The Effect of the Elliptic Polarization on the Quasi-particle Dynamics of Linearly Coupled Systems of Nonlinear Schroedinger Equations