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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2000-2001 MATHEMATICS COLLOQUIUM SERIES DEPARTMENT OF MATHEMATICS JOINT WITH THE SCHOOL OF OPTICS 03/29/01 Colloquium DR. JIANKE YANG DEPARTMENT OF MATHEMATICS UNIVERSITY OF VERMONT Complexity of Vector-Soliton Collisions Abstract: In this talk, we discuss complexities and regularities of vector-soliton collisions in the context of non-integrable coupled nonlinear Schroedinger equations. We show that for collisions of orthogonally polarized and equal-amplitude vector solitons, the exit-velocity versus collision-velocity graph has a fractal structure in certain ranges of the cross-phase-modulational (XPM) coefficient. When we zoom into different positions of this fractal, we get structures which are either a copy, a horizontal reflection or vertical reflection of the original structure. Collision dynamics in the zoomed-in windows and that in the original graph follow simple and well-defined patterns as well. At lower ranges of the XPM coefficient, this fractal structure reduces to a sequence of resonance windows similar to that in the phi-4 model. We explain these collision structures by a simple variational model where a resonance between translational motion and width oscillations of vector solitons is held responsible for fractal dependence of vector-soliton collisions. Results on collisions of unequal-amplitude and non-orthogonal vector solitons will also be presented.