Complexity and regularity of vector-soliton collisions.

In this paper, we extensively investigate the collision of vector solitons in the coupled nonlinear Schrödinger equations. First, we show that for collisions of orthogonally polarized and equal-amplitude vector solitons, when the cross-phase modulational coefficient beta is small, a sequence of reflection windows similar to that in the phi(4) model arises. When beta increases, a fractal structure unlike phi(4)'s gradually emerges. But when beta is greater than one, this fractal structure disappears. Analytically, we explain these collision behaviors by a variational model that qualitatively reproduces the main features of these collisions. This variational model helps to establish that these window sequences and fractal structures are caused entirely or partially by a resonance mechanism between the translational motion and width oscillations of vector solitons. Next, we investigate collision dependence on initial polarizations of vector solitons. We discovered a sequence of reflection windows that is phase induced rather than resonance induced. Analytically, we have derived a simple formula for the locations of these phase-induced windows, and this formula agrees well with the numerical data. Last, we discuss collision dependence on relative amplitudes of initial vector solitons. We show that when vector solitons have different amplitudes, the collision structure simplifies. Feasibility of experimental observation of these results is also discussed at the end of the paper.