A New Discrete Hénon-Heiles System

DOI

10.2991/jnmp.2003.10.s2.3How to use a DOI?

Abstract

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Alan K. Common
AU  - Andrew N.W. Hone
AU  - Micheline Musette
PY  - 2003
DA  - 2003/12/01
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  - 10.2991/jnmp.2003.10.s2.3
ID  - Common2003
ER  -