Localization of chaos in the discrete nonlinear Schrödinger equation.

Abstract

We partition the perturbation phase space in the three-element discrete nonlinear Schr\odinger equation into symmetric and antisymmetric subspaces. We then show that chaotic motion in the neighborhood of symmetric trajectories is confined to the antisymmetric space. Chaos occurs in the system at arbitrarily low levels of nonlinearity, in agreement with previous calculations. We call this phenomenon ``microchaos.''