On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term

Details On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term

2004-02-18

arxiv.org/abs/math-ph/0402049v1

Phys.Atom.Nucl. 68 (2005) 1947-1955; Yad.Fiz. 68 (2005) 2008-2016

Physics

Mathematical Physics

LaTeX2e, 12pp

Scientific paper

The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies search of the elliptic solutions and allows to automatize it.

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