The dynamics of complex-amplitude norm-preserving lattices of coupled oscillators

We introduce a class of models composed by lattices of coupled complex-amplitude oscillators which preserve the norm. These models are particularly well adapted to investigate phenomena described by the nonlinear Schrödinger equation. The coupling between oscillators is parameterized by the mass, while their local dynamics is illustrated for two area-preserving maps: one obtained from the exact local solution of the Schrödinger equation, the other obtained from its Crank–Nicholson discretization. In both cases, we determine all periodic orbits and show how to detect artifacts introduced by the discretization.