Abstract
We address (i) the onset of spatiotemporal chaos (STC) induced by the hyperbolic structure in a weakly perturbed nonlinear Schrödinger equation, and (ii) its effective stochastic dynamics (ESD). We obtain the following new results: (1) a very small number ( two for our system) of linearly unstable modes is sufficient to trigger the onset of STC as characterized by an exponential decay in space of the mutual information; (2) the construction of the ESD needs only temporal chaos, in contrast to the requirement of full STC as usually believed.
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