Elliptic solutions in the H\'{e}non - Heiles model
Exactly Solvable and Integrable Systems
2012-08-06 v1
Abstract
Equations of motion corresponding to the H\'{e}non - Heiles system are considered. A method enabling one to find all elliptic solutions of an autonomous ordinary differential equation or a system of autonomous ordinary differential equations is described. New families of elliptic solutions of a fourth--order equation related to the H\'{e}non - Heiles system are obtained. A classification of elliptic solutions up to the sixth order inclusively is presented.
Cite
@article{arxiv.1208.0726,
title = {Elliptic solutions in the H\'{e}non - Heiles model},
author = {Maria V. Demina and Nikolai A. Kudryashov},
journal= {arXiv preprint arXiv:1208.0726},
year = {2012}
}