Dynamical systems techniques have tremendous potential for application in the area of nonlinear optics. Important problems of optical communication, such as the stability of pulse propagation and locking of multiple pulses can be formulated as problems susceptible to the modern geometric techniques of dynamical systems. This proposal involves a collaboration with a German group headed by Tassilio K¼pper of the University of Cologne. One goal of the collaboration is to involve graduate students in the research and expose them to both sides of the work through travel to Germany. Problems considered will be the stability of nonlinear waveguide modes relative to the full Maxwell- Bloch system, multiple pulse propagation, and the locking of pulses on coupled fibers. Techniques used will be bifurcation theory, stability indices, bifurcation from the essential spectrum, and numerical investigations.
