Separability and Lax pairs for the two-dimensional Hamiltonian system with a quartic potential
- 1 July 1995
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 36 (7), 3559-3565
- https://doi.org/10.1063/1.530981
Abstract
The two-dimensional Hamiltonian system with a quartic potential is known to be integrable in four cases, that is, for four sets of parameter values. In three of these cases the system is also known to be separable. In this paper, separating variables for the fourth integrable case are obtained, allowing its solution in terms of elliptic functions. Lax pairs with a spectral parameter for the four integrable cases are also obtained.Keywords
This publication has 9 references indexed in Scilit:
- Generalized separability for a Hamiltonian with nonseparable quartic potentialPhysics Letters A, 1994
- Separability and Lax pairs for Hénon–Heiles systemJournal of Mathematical Physics, 1993
- Painlevé analysis, Lie symmetries, and integrability of coupled nonlinear oscillators of polynomial typePhysics Reports, 1993
- The Painlevé property and singularity analysis of integrable and non-integrable systemsPhysics Reports, 1989
- Direct methods for the search of the second invariantPhysics Reports, 1987
- Integrability of One Particle in a Perturbed Central Quartic PotentialPhysica Scripta, 1985
- Extension of the class of integrable dynamical systems connected with semisimple Lie algebrasLetters in Mathematical Physics, 1985
- On the Olshanetsky-Perelomov many-body system in an external fieldPhysics Letters A, 1984
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968