Complexity and regularity of vector-soliton collisions - art. no. 056616

In this paper, we extensively investigate the collision of vector solitons in the coupled nonlinear Schrodinger equations. First, we show that for col lisions of orthogonally polarized and equal-amplitude vector solitons, when the cross-phase modulational coefficient beta is small, a sequence of refl ection windows similar to that in the phi (4) model arises. When beta incre ases, a fractal structure unlike phi (4,)s gradually emerges. But when beta is greater than one, this fractal structure disappears. Analytically, we e xplain these collision behaviors by a variational model that qualitatively reproduces the main features of these collisions. This variational model he lps to establish that these window sequences and fractal structures are cau sed entirely or partially by a resonance mechanism between the translationa l motion and width oscillations of vector solitons. Next, we investigate co llision dependence on initial polarizations of vector solitons. We discover ed a sequence of reflection windows that is phase induced rather than reson ance induced. Analytically, we have derived a simple formula for the locati ons of these phase-induced windows, and this formula agrees well with the n umerical data. Last, we discuss collision dependence on relative amplitudes of initial vector solitons. We show that when vector solitons have differe nt amplitudes, the collision structure simplifies. Feasibility of experimen tal observation of these results is also discussed at the end of the paper.