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Polarization dynamics during takeover collisions of solitons in systems of coupled nonlinears Schödinger equations
For the system of coupled nonlinear Schrödinger equations we investigate
numerically the takeover interaction dynamics of elliptically polarized
solitons. In the case of general elliptic polarization, analytical solution for the
shapes of a steadily propagating solitons are not available, and we develop a
numerical algorithm finding the shape. We use the superposition of generally
elliptical polarized solitons as the initial condition for investigating the soliton
dynamics. In order to extract the pure effect of the initial phase angle, we
consider the case without cross-modulation – the Manakov system. The sum
of the masses for the two quasi-particles is constant and the total pseudomementum
and energy of the system are conserved. In the case of nontrivial
cross-modulation combining it with different initial phase angles causes velocity
shifts of interacted solitons. The results of this work outline the role of
the initial phase, initial polarization and the interplay between them and nonlinear
couplings on the interaction dynamics of solitons in system of coupled
nonlinear Schrödinger equations.