  In this work we explore how nonlinear modes described by a dispersive wave
equation (in our example, the nonlinear Schrodinger equation) and localized in
a few wells of a periodic potential can act analogously to a chain of coupled
mechanical oscillators. We identify the small-amplitude oscillation modes of
these `coupled wave oscillators' and find that they can be extended into the
large amplitude regime, where some can `ring' for long times. We also identify
prototypical case examples of more complex dynamical behaviour that can arise
in such systems beyond the double well paradigm, including the breakdown of
Josephson-like oscillations and of internal modes more generally, the transfer
of energy out of/destabilization of fundamental oscillation modes and the
emergence of chaotic oscillations for large amplitude excitations. We provide
details of the phase perturbations required for experimental observations of
such dynamics, and show that the oscillator formalism can be extended to
predict large amplitude excitations in genuinely two-dimensional
configurations.
