PREPRINT
874CBE4B-72E9-470D-BBA8-F18017E69BAD

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

E. I. Timoshkova, S. Yu. Vernov
arXiv:math-ph/0402049

Submitted on 18 February 2004

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.

Preprint

Comment: LaTeX2e, 12pp

Subjects: Mathematical Physics; Astrophysics; Nonlinear Sciences - Exactly Solvable and Integrable Systems

URL: https://arxiv.org/abs/math-ph/0402049