Exact solutions for a class of integrable Henon-Heiles-type systems

TL;DR

This paper derives exact solutions for a class of integrable Henon-Heiles-type systems using Kleinian and Weierstrass functions, extending results to systems with multiple degrees of freedom.

Contribution

It provides explicit solutions for integrable Henon-Heiles systems and generalizes these results to systems with more degrees of freedom.

Findings

Solutions expressed in terms of Kleinian functions

Periodic solutions in terms of Weierstrass functions

Extension to systems with n+1 degrees of freedom

Abstract

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.