### Abstract

The cubic Schrödinger equation is considered on the circle, both in the de-focussing and the focussing case. The existence of the flow is proved together with the invariance of the appropriate Gibbsian measure, namely the petit canonical measure in the defocussing case and the micro-canonical measure in the focussing case.

Original language | English (US) |
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Pages (from-to) | 479-491 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

Volume | 168 |

Issue number | 3 |

DOIs | |

State | Published - Apr 1995 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*168*(3), 479-491. https://doi.org/10.1007/BF02101840

**Statistical mechanics of nonlinear wave equations (4) : Cubic Schrödinger.** / McKean, H. P.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 168, no. 3, pp. 479-491. https://doi.org/10.1007/BF02101840

}

TY - JOUR

T1 - Statistical mechanics of nonlinear wave equations (4)

T2 - Cubic Schrödinger

AU - McKean, H. P.

PY - 1995/4

Y1 - 1995/4

N2 - The cubic Schrödinger equation is considered on the circle, both in the de-focussing and the focussing case. The existence of the flow is proved together with the invariance of the appropriate Gibbsian measure, namely the petit canonical measure in the defocussing case and the micro-canonical measure in the focussing case.

AB - The cubic Schrödinger equation is considered on the circle, both in the de-focussing and the focussing case. The existence of the flow is proved together with the invariance of the appropriate Gibbsian measure, namely the petit canonical measure in the defocussing case and the micro-canonical measure in the focussing case.

UR - http://www.scopus.com/inward/record.url?scp=21844524171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844524171&partnerID=8YFLogxK

U2 - 10.1007/BF02101840

DO - 10.1007/BF02101840

M3 - Article

AN - SCOPUS:21844524171

VL - 168

SP - 479

EP - 491

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -