2004/02/18 by E. I. Timoshkova, S. Yu. Vernov · 6 citations
Chemistry · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Laurent series #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Series (stratigraphy) #Singularity #Term (time) #astro-ph #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1134/1.2131124
published in Physics of Atomic Nuclei 68(11), 1947-1955 (Pleiades Publishing) · LaTeX2e, 12pp
arxiv created 2004/02/18 · openalex publication_date 2005/11/01 · arxiv updated 2013/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The generalized Hénon-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 searches for the elliptic solutions and allows them to be automatized.