We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected, transmitted, or captured by the defect. We propose a mechanism of resonant energy transfer to a nonlinear standing wave mode supported by the defect. Following Forinash et al, we derive a finite-dimensional model for the interaction of the soliton with the defect via a collective coordinates method. The system thus derived is a three degree-of-freedom Hamiltonian with an additional conserved quantity. We study this system using the tools of dynamical systems theory, and find that it exhibits a variety of interesting behaviors, largely determined by the structures of stable and unstable manifolds of special classes of periodic orbits. We use this geometrical understanding to interpret the simulations.

21 pages, 14 figures, Invited paper for Mathematics as a Guide to the Understanding of Applied Nonlinear Problems, a conference in honor of Klaus Kirchgassner's 70th birthday, Kloster Irsee, Germany, Jan 6-10, 2002