Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector NLSE

For the Coupled Nonlinear Schrödinger Equations (CNLSE) we construct a conservative fully implicit scheme (in the vein of the scheme with internal iterations proposed in [C.I. Christov, S. Dost, G.A. Maugin, Inelasticity of soliton collisions in system of coupled nls equations, Physica Scripta 50 (1994) 449–454.]). Our scheme makes use of complex arithmetic which allows us to reduce the computational time fourfold. The scheme conserves the “mass”, momentum, and energy. We investigate collisions of solitary waves (quasi-particles or QPs) with linear polarization in the initial configuration. We elucidate numerically the role of nonlinear coupling on the quasi-particle dynamics. We find that the initially linear polarizations of the QPs change after the collision to elliptic polarizations. For large values of cross-modulation parameter, an additional QP is created during the collision. We find that although the total energy is positive and conserved, the energy only of the system of identifiable after the collision QPs is negative, i.e., the different smaller excitations and radiation carry away part of the energy. The effects found in the present work shed light on the intimate mechanisms of interaction of QPs. © 2009 IMACS. Published by Elsevier B.V. All rights reserved. PACS: 02.70.-c; 05.45.Yv; 42.65.Tg