Painlevé property and integrability

Nicholas Ercolani; Eric D. Siggia

doi:10.1016/0375-9601(86)90426-3

Painlevé property and integrability

Nicholas Ercolani, Eric D. Siggia

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

21 Scopus citations

Abstract

For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

Original language	English (US)
Pages (from-to)	112-116
Number of pages	5
Journal	Physics Letters A
Volume	119
Issue number	3
DOIs	https://doi.org/10.1016/0375-9601(86)90426-3
State	Published - Dec 8 1986

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/0375-9601(86)90426-3

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title = "Painlev{\'e} property and integrability",

abstract = "For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.",

author = "Nicholas Ercolani and Siggia, {Eric D.}",

note = "Funding Information: Rand, and J. Sethna for helpful remarks. The integrals for KdV were provided by Flaschka. Our research was supportedby the Department ofEnergy (Grant No. HDE-ACO2-83-ER), the National Science Foundation (Grant Nos. DMR-83 14625 and DMS-84 14092) and the Institute for Theoretical Physics in Santa Barbara.",

year = "1986",

month = dec,

day = "8",

doi = "10.1016/0375-9601(86)90426-3",

language = "English (US)",

volume = "119",

pages = "112--116",

journal = "Physics Letters A",

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TY - JOUR

T1 - Painlevé property and integrability

AU - Ercolani, Nicholas

AU - Siggia, Eric D.

N1 - Funding Information: Rand, and J. Sethna for helpful remarks. The integrals for KdV were provided by Flaschka. Our research was supportedby the Department ofEnergy (Grant No. HDE-ACO2-83-ER), the National Science Foundation (Grant Nos. DMR-83 14625 and DMS-84 14092) and the Institute for Theoretical Physics in Santa Barbara.

PY - 1986/12/8

Y1 - 1986/12/8

N2 - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

AB - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

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U2 - 10.1016/0375-9601(86)90426-3

DO - 10.1016/0375-9601(86)90426-3

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VL - 119

SP - 112

EP - 116

JO - Physics Letters A

JF - Physics Letters A

IS - 3

ER -

Painlevé property and integrability

Abstract

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