TY - JOUR
T1 - Spatiotemporal chaos and effective stochastic dynamics for a near-integrable nonlinear system
AU - Cai, David
AU - McLaughlin, David W.
AU - Shatah, Jalal
N1 - Funding Information:
The three authorsr eceived support from the Sloan Foundation under a grant entitled “Indeterminacy in Large Systems: Chaotic and Random Behavior”. In addition Dr. McLaughlin receivedp artial supportf rom the National Science Foundation (DMS-9600128) and from the AFOSR (grant #F49620-98-l -0256). Dr. Shatah received partial support from the NSF (DMS-9401558).
PY - 1999/3/29
Y1 - 1999/3/29
N2 - 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.
AB - 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.
KW - Integrability
KW - Mutual information
KW - NLS
KW - Spatiotemporal chaos
KW - Stochastic dynamics
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U2 - 10.1016/S0375-9601(99)00057-2
DO - 10.1016/S0375-9601(99)00057-2
M3 - Article
AN - SCOPUS:0004456563
SN - 0375-9601
VL - 253
SP - 280
EP - 286
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 5-6
ER -