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04/03/03 Colloquium
DR. PANAYOTIS PANAYOTAROS
UNIVERSITY OF COLORADO AT BOULDER
UNIVERSITY OF COLORADO AT BOULDER
Birkhoff Normal Forms for the Periodic Dispersion Managed Nonlinear Schrodinger Equation
Abstract: We describe recent work on the dispersion managed nonlinear Schrodinger (DMNLS) equation, a non-autonomous evolution system that models the propagation of signals in optical fibers. We consider periodic boundary conditions, and use averaging ideas and the Hamiltonian structure of the DMNLS system to construct normal form equations that are simpler to analyze. For example, normal form systems are seen to possess families of periodic orbits, and we can also answer some stability questions. We also give error estimates for the solutions of the quartic normal form system.