Michael Weinstein

Columbia University
ABSTRACT:
An important class of mathematical resonance problems arises for
Hamiltonian partial differential equations, which may be viewed as
consisting of two coupled subsystems: a finite dimensional part
governing "oscillators" with discrete frequencies and an infinite
dimensional part, governing "waves" with a continuous spectrum of
frequencies. We first discuss several examples and then describe work
on ground state selection and energy equi-partition for nonlinear
Schroedinger / Gross-Pitaevskii equations. Finally, we discuss
confirmation of predictions in nonlinear optical experiments.