Abstract
We consider several discretizations of the nonlinear Schrödinger equation which lead naturally to the study of some symmetric difference equations of the form φn+1+φn-1 = f(φn). We find a variety of interesting and exotic behaviour from simple closed orbits to intricate patterns of orbits and loops in the (φn+1,φn) phase-plane. Some analytical results for a special case are also presented.
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