Polarization dynamics during takeover collisions of solitons in systems of coupled nonlinears Schödinger equations

Pages: 1385 - 1394, Issue Special, September 2011

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M. D. Todorov - Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria (email)

Abstract: 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.

Keywords:  SCNLSE, Elliptic polarization, Collision dynamics, Takeover
Mathematics Subject Classification:  Primary: 65M06, 35Q55; Secondary: 35Q51

Received: July 2010;      Revised: April 2011;      Published: October 2011.