### 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 (US) |
---|---|

Pages (from-to) | 280-286 |

Number of pages | 7 |

Journal | Physics Letters A |

Volume | 253 |

Issue number | 5-6 |

State | Published - Mar 29 1999 |

### Fingerprint

### Keywords

- Integrability
- Mutual information
- NLS
- Spatiotemporal chaos
- Stochastic dynamics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*253*(5-6), 280-286.

**Spatiotemporal chaos and effective stochastic dynamics for a near-integrable nonlinear system.** / Cai, David; McLaughlin, David W.; Shatah, Jalal.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 253, no. 5-6, pp. 280-286.

}

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

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 - http://www.scopus.com/inward/record.url?scp=0004456563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004456563&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0004456563

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

SN - 0375-9601

IS - 5-6

ER -