On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term
arXiv:math-ph/0402049 · doi:10.1134/1.2131124
Abstract
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.
LaTeX2e, 12pp