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TMF, 2003, Volume 134, Number 1, Pages 148–159 (Mi tmf147)  

This article is cited in 9 scientific papers (total in 9 papers)

General Solution for Hamiltonians with Extended Cubic and Quartic Potentials

C. Verhoevena, M. Musettea, R. Conteb

a Vrije Universiteit
b CEA, Service de Physique Théorique

Abstract: In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases $1:6:1$ and $1:6:8$.

Keywords: Hénon–Heiles, Hamiltonian systems, separation of variables, nonlinear equations, hyperelliptic functions, soliton equations

DOI: https://doi.org/10.4213/tmf147

Full text: PDF file (220 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 134:1, 128–138

Bibliographic databases:


Citation: C. Verhoeven, M. Musette, R. Conte, “General Solution for Hamiltonians with Extended Cubic and Quartic Potentials”, TMF, 134:1 (2003), 148–159; Theoret. and Math. Phys., 134:1 (2003), 128–138

Citation in format AMSBIB
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\paper General Solution for Hamiltonians with Extended Cubic and Quartic Potentials
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\jour Theoret. and Math. Phys.
\yr 2003
\vol 134
\issue 1
\pages 128--138
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Musette, C. Verhoeven, “$C$-KP and $B$-KP Equations Related to the Generalized Quartic Hénon–Heiles Hamiltonian”, Theoret. and Math. Phys., 137:2 (2003), 1561–1573  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Timoshkova E.I., Vernov S.Y., “The Painlevé analysis and construction of solutions for the generalized Henon-Heiles system”, Order and Chaos in Stellar and Planetary Systems, Astronomical Society of the Pacific Conference Series, 316, 2004, 28–33  adsnasa  isi
    3. R. Conte, M. Musette, C. Verhoeven, “Completeness of the Cubic and Quartic Henon–Heiles Hamiltonians”, Theoret. and Math. Phys., 144:1 (2005), 888–898  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Vernov SY, Timoshkova EI, “On two nonintegrable cases of the generalized Henon-Heiles system”, Physics of Atomic Nuclei, 68:11 (2005), 1947–1955  crossref  mathscinet  adsnasa  isi  scopus  scopus
    5. Vernov, SY, “Construction of special solutions for nonintegrable systems”, Journal of Nonlinear Mathematical Physics, 13:1 (2006), 50  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Verhoeven C., Musette M., Conte R., “On reductions of some KdV-type systems and their link to the quartic Henon-Heiles Hamiltonian”, Bilinear Integrable Systems: From Classical to Quatum, Continuous to Discrete, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 201, 2006, 363–374  mathscinet  zmath  isi
    7. Lesfari, A, “CYCLIC COVERINGS OF ABELIAN VARIETIES AND THE GENERALIZED YANG-MILLS SYSTEM FOR A FIELD WITH GAUGE GROUP SU(2)”, International Journal of Geometric Methods in Modern Physics, 5:6 (2008), 947  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Claeys T., Doeraene A., “The Generating Function For the Airy Point Process and a System of Coupled Painlevé II Equations”, Stud. Appl. Math., 140:4 (2018), 403–437  crossref  mathscinet  isi  scopus  scopus
    9. Lesfari A., “Geometric Study of a Family of Integrable Systems”, Int. Electron. J. Geom., 11:1 (2018), 78–92  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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