SIGMA 2 (2006), 064, 4 pages nlin.SI/0408027
On a 'Mysterious' Case of a Quadratic Hamiltonian
Institute of Physics, National Academy of Sciences, 220072 Minsk, Belarus
Received June 02, 2006, in final form July 18, 2006; Published online July 28, 2006
We show that one of the five cases of a quadratic
Hamiltonian, which were recently selected by Sokolov and Wolf who
used the Kovalevskaya-Lyapunov test, fails to pass the
Painlevé test for integrability.
Hamiltonian system; nonintegrability; singularity analysis.
pdf (138 kb)
ps (107 kb)
tex (7 kb)
- Sokolov V.V., Wolf T., Integrable quadratic classical Hamiltonians
on so(4) and so(3,1), J. Phys. A: Math. Gen., 2006,
V.39, 1915-1926, nlin.SI/0405066.
- Ablowitz M.J., Ramani A., Segur H., A connection between
nonlinear evolution equations and ordinary dif ferential
equations of P-type. I, J. Math. Phys., 1980, V.21,
- Ramani A., Grammaticos B., Bountis T., The Painlevé
property and singularity analysis of integrable and non-integrable
systems, Phys. Rep., 1989, V.180, 159-245.
- Tsiganov A.V., Goremykin O.V., Integrable systems on so(4) related with XXX
spin chains with boundaries, J. Phys. A: Math. Gen., 2004,
V.37, 4843-4849, nlin.SI/0310049.
- Sokolov V.V., On a class of quadratic Hamiltonians on so(4), Dokl. Akad. Nauk,
2004, V.394, 602-605 (in Russian).
- Ramani A., Dorizzi B., Grammaticos B., Painlevé conjecture revisited,
Phys. Rev. Lett., 1982, V.49, 1539-1541.
- Grammaticos B., Dorizzi B., Ramani A., Integrability of
Hamiltonians with third- and fourth-degree polynomial potentials,
J. Math. Phys., 1983, V.24, 2289-2295.
- Ablowitz M.J., Clarkson P.A., Solitons, nonlinear evolution equations and inverse
scattering, Cambridge, Cambridge University Press, 1991.
- Sakovich S.Yu., Tsuchida T., Symmetrically coupled higher-order
nonlinear Schrödinger equations: singularity analysis and
integrability, J. Phys. A: Math. Gen.,
2000, V.33, 7217-7226, nlin.SI/0006004.
- Sakovich S.Yu., Tsuchida T., Coupled higher-order
nonlinear Schrödinger equations: a new integrable case via the
singularity analysis, nlin.SI/0002023.