  We investigate numerically by a conservative difference scheme in complex
arithmetic the head-on and takeover collision dynamics of the solitary waves as
solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various
initial phases. The initial conditions are superposition of two one-soliton
solutions with general polarization. The quasi-particle behavior of propagating
and interacting solutions in conditions of rotational polarization is examined.
We find that the total mass, pseudomomentum and energy are conserved while the
local masses, individual and total polarization depend strongly on the linear
coupling and the initial phase difference. We also find out that the
polarization angle of the quasi-particles can change independently of the
interaction.
