Integrable Hamiltonian systems and the Painlevé property

Tassos Bountis, Harvey Segur, Franco Vivaldi

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172 Citations (Scopus)

Abstract

A direct method is described for obtaining conditions under which certain N-degree-of-freedom Hamiltonian systems are integrable, i.e., possess N integrals in involution. This method consists of requiring that the general solutions have the Painlevé property, i.e., no movable singularities other than poles. We apply this method to several Hamiltonian systems of physical significance such as the generalized Hénon-Heiles problem and the Toda lattice with N=2 and 3, and recover all known integrable cases together with a few new ones. For some of these cases the second integral is written down explicitly while for others integrability is confirmed by numerical experiments.

Original languageEnglish
Pages (from-to)1257-1264
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume25
Issue number3
DOIs
Publication statusPublished - 1982
Externally publishedYes

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degrees of freedom

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Integrable Hamiltonian systems and the Painlevé property. / Bountis, Tassos; Segur, Harvey; Vivaldi, Franco.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 25, No. 3, 1982, p. 1257-1264.

Research output: Contribution to journalArticle

Bountis, Tassos ; Segur, Harvey ; Vivaldi, Franco. / Integrable Hamiltonian systems and the Painlevé property. In: Physical Review A - Atomic, Molecular, and Optical Physics. 1982 ; Vol. 25, No. 3. pp. 1257-1264.
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