  The nonlinear Schr\"odinger/Gross-Pitaevskii (NLS/GP) equation is considered
in the presence of three equally-spaced potentials. The problem is reduced to a
finite-dimensional Hamiltonian system by a Galerkin truncation. Families of
oscillatory orbits are sought in the neighborhoods of the system's nine
branches of standing wave solutions. Normal forms are computed in the
neighborhood of these branches' various Hamiltonian Hopf and saddle-node
bifurcations, showing how the oscillatory orbits change as a parameter is
increased. Numerical experiments show agreement between normal form theory and
numerical solutions to the reduced system and NLS/GP near the Hamiltonian Hopf
bifurcations and some subtle disagreements near the saddle-node bifurcations
due to exponentially small terms in the asymptotics.
