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

David Cai; David W. McLaughlin; Jalal Shatah

doi:10.1016/S0375-9601(99)00057-2

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

David Cai
, David W. McLaughlin
, Jalal Shatah

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	280-286
Number of pages	7
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	253
Issue number	5-6
DOIs	https://doi.org/10.1016/S0375-9601(99)00057-2
State	Published - 29 Mar 1999
Externally published	Yes

Keywords

Integrability
Mutual information
NLS
Spatiotemporal chaos
Stochastic dynamics

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10.1016/S0375-9601(99)00057-2

Cite this

@article{13a76e8cc5e941089f1ec54ecc67a1c7,

title = "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 Schr{\"o}dinger 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.",

keywords = "Integrability, Mutual information, NLS, Spatiotemporal chaos, Stochastic dynamics",

author = "David Cai and McLaughlin, \{David W.\} and Jalal Shatah",

note = "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).",

year = "1999",

month = mar,

day = "29",

doi = "10.1016/S0375-9601(99)00057-2",

language = "English",

volume = "253",

pages = "280--286",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "5-6",

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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

UR - https://www.scopus.com/pages/publications/0004456563

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 -

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

Abstract

Keywords

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