Volume 10, Issue Supplement 2, December 2003, Pages 27 - 40
A New Discrete Hénon-Heiles System
Alan K. Common, Andrew N.W. Hone, Micheline Musette
Alan K. Common
Available Online 1 December 2003.
- https://doi.org/10.2991/jnmp.2003.10.s2.3How to use a DOI?
- By considering the Darboux transformation for the third order Lax operator of the Sawada-Kotera hierarchy, we obtain a discrete third order linear equation as well as a discrete analogue of the Gambier 5 equation. As an application of this result, we consider the stationary reduction of the fifth order Sawada-Kotera equation, which (by a result of Fordy) is equivalent to a generalization of the integrable case (i) HénoHeiles system. Applying the Darboux transformation to the stationary flow, we find a Bäcklund transformation (BT) for this finite-dimensional Hamiltonian system, which is equivalent to an exact discretization of the generalized case (i) Hénon-Heiles system. The Lax pair for the system is 3 × 3, and the BT satisfies the spectrality property for the associated trigonal spectral curve. We also give an example of how the BT may be used as a numerical integrator for the original continuous Hénon-Heiles system.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Alan K. Common AU - Andrew N.W. Hone AU - Micheline Musette PY - 2003 DA - 2003/12 TI - A New Discrete Hénon-Heiles System JO - Journal of Nonlinear Mathematical Physics SP - 27 EP - 40 VL - 10 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2003.10.s2.3 DO - https://doi.org/10.2991/jnmp.2003.10.s2.3 ID - Common2003 ER -