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Some Nearly Finite-Dimensional Hamiltonian Dynamics in NLS-like Systems

By Roy Goodman, New Jersey Institute of Technology

We will talk about two physical systems where the dynamics, though infinite-dimensional, is well approximated by a small Hamiltonian system of ODE. The first is the nonlinear Schrödinger/Gross-Pitaevskii equation with a multiple-well localized potential. Here we show how how Hamiltonian Hopf bifurcations lead to novel quasiperiodic orbits and chaotic dynamics. The second is vortex interactions in a two-dimensional Bose-Einstein condensate, where we find homoclinic chaos leading to stochastic reversals in the direction of rotation of a pair of rotating vortices.