Non-autonomous H\'{e}non-Heiles Systems
solv-int
2009-10-30 v1 Exactly Solvable and Integrable Systems
Abstract
Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable H\'{e}non-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivatives of the tau-functions (inherited from the original PDEs). The ODEs for the similarity solutions also have inherited B\"{a}cklund transformations, which may be used to generate sequences of rational solutions as well as other special solutions related to the first Painlev\'{e} transcendent.
Keywords
Cite
@article{arxiv.solv-int/9703005,
title = {Non-autonomous H\'{e}non-Heiles Systems},
author = {Andrew N. W. Hone},
journal= {arXiv preprint arXiv:solv-int/9703005},
year = {2009}
}
Comments
25 pages, Latex. Some minor corrections