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

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.

preprint2004arXivOpen access
E. I. TimoshkovaS. Yu. Vernov
astro-phmath-phmath.MPnlin.SI
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E. I. TimoshkovaS. Yu. Vernov

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