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In this work we explore how nonlinear modes described by a dispersive waveequation (in our example, the nonlinear Schrodinger equation) and localized ina few wells of a periodic potential can act analogously to a chain of coupledmechanical oscillators. We identify the small-amplitude oscillation modes ofthese `coupled wave oscillators' and find that they can be extended into thelarge amplitude regime, where some can `ring' for long times. We also identifyprototypical case examples of more complex dynamical behaviour that can arisein such systems beyond the double well paradigm, including the breakdown ofJosephson-like oscillations and of internal modes more generally, the transferof energy out of/destabilization of fundamental oscillation modes and theemergence of chaotic oscillations for large amplitude excitations. We providedetails of the phase perturbations required for experimental observations ofsuch dynamics, and show that the oscillator formalism can be extended topredict large amplitude excitations in genuinely two-dimensionalconfigurations.

Going beyond the double well: complex mode dynamics of effective coupled oscillators in infinite dimensional systems