Spatiotemporal chaos and effective stochastic dynamics for a near-integrable nonlinear system

Abstract

We address (i) the onset of spatiotemporal chaos (STC) induced by the hyperbolic structure in a weakly perturbed nonlinear Schrijdinger 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 remporal chaos, in contrast to the requirement of full STC as usually believed. @ 1999 Elsevier Science B.V. PACS: 03.40.Kf; 05.45.+b; 05.70.Ln; 82.4O.Bj

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@inproceedings{Cai1999SpatiotemporalCA, title={Spatiotemporal chaos and effective stochastic dynamics for a near-integrable nonlinear system}, author={David Cai and David W. McLaughlin and Jalal Shatah}, year={1999} }