The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled systems of Nonlinear Schrödinger Equations

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 Schrödinger Equations for various initial phases. The initial conditions are superposition of two one-soliton solutions with arbitrary (elliptic) polarization. The quasi-particle behavior of propagating and interacting solutions in conditions of elliptic and rotational polarizations at once 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.