Consecutive Rosochatius deformations of the Neumann system are investigated. It is first shown that different realizations of a classical sl(2) Gaudin magnet model yield different integrable Hamiltonian systems. Then an algorithm of constructing infinitely many symplectic realizations of sl(2) algebra from a known one is presented and thus the Neumann system can be deformed consecutively. The second Rosochatius deformation of the Neumann system is taken as an illustrative example to show that the deformed systems admit separations of variables and may be linearized on the Jacobi variety.
REFERENCES
1.
J.
Moser
, “Various aspects of integrable Hamiltonian systems
,” in Dynamical Systems
, CIME Lectures, edited by J.
Guckenheimer
, J.
Moser
, and S. E.
Newhouse
(Birkhäuser
, 1980
).2.
3.
J.
Moser
, “Geometry of quadrics and spectral theory
,” in The Chern Symposium 1979, Proceedings of the International Symposium, Berkley, CA, 1979
(Springer
, 1980
), pp. 147
–188
.4.
E. K.
Sklyanin
, Prog. Theor. Phys. Suppl.
118
, 35
(1995
).5.
O.
Babelon
and C. M.
Viallet
, Phys. Lett. B
237
, 411
(1990
).6.
O.
Babelon
and M.
Talon
, Nucl. Phys. B
379
, 321
(1992
).7.
J.
Harnad
and P.
Winternitz
, Commun. Math. Phys.
172
, 263
(1995
).8.
O.
Ragnisco
and Y.
Suris
, Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman
(Birkhäuser
, 1996
), pp. 285
–300
.9.
M.
Antonowicz
and S.
Rauch-Wojciechowski
, Inverse Probl.
9
, 201
(1993
).10.
E.
Rosochatius
, Ph.D. dissertation, University of Götingen
, 1877
.11.
G.
Arutyunov
, J.
Russo
, and A. A.
Tseytlin
, Phys. Rev. D
69
, 086009
(2004
).12.
H.
Dimov
and R.
Rashkov
, Int. J. Mod. Phys. A
20
, 4337
(2005
).13.
P.
Bozhilov
, J. High Energy Phys.
2007
(8
), 073
.14.
N. A.
Kostov
, Lett. Math. Phys.
17
, 95
(1989
).15.
P. L.
Christiansen
, J. C.
Eilbeck
, V. Z.
Enolskii
, and N. A.
Kostov
, Proc. R. Soc. London, Ser. A
456
, 2263
(2000
).16.
T.
Ratiu
, AIP Conf. Proc.
88
, 109
–115
(1982
).17.
M. R.
Adams
, J.
Harnad
, and E.
Previato
, Commun. Math. Phys.
117
, 451
(1988
).18.
S.
Wojciechowski
, Phys. Scr.
31
, 433
(1985
).19.
G.
Tondo
, J. Phys. A
28
, 5097
(1995
).20.
R.
Kubo
, W.
Ogura
, T.
Saito
, and Y.
Yasui
, Phys. Lett. A
251
, 6
(1999
).21.
C.
Bartocci
, G.
Falqui
, and M.
Pedroni
, Diff. Geom. Applic.
21
, 349
(2004
).22.
C. W.
Cao
and B. Q.
Xia
, Commun. Theor. Phys.
54
, 619
(2010
).23.
Y. Q.
Yao
and Y. B.
Zeng
, J. Phys. A: Math. Theor.
41
, 295205
(2008
).24.
R. G.
Zhou
, J. Math. Phys.
48
, 103510
(2007
).25.
B. Q.
Xia
and R. G.
Zhou
, Phys. Lett. A
373
, 4360
(2009
).26.
V. B.
Kuznetsov
, J. Math. Phys.
33
, 3240
(1992
).27.
J. C.
Eilbeck
, V. Z.
Enolskii
, V. B.
Kuznetsov
, and A. V.
Tsiganov
, J. Phys. A
27
, 567
(1994
).28.
K.
Sundermeyer
, in General Relativity, Classical Spin, Dual String Model
, Lectures Notes in Physics
(Springer-Verlag
, 1982
).29.
R. G.
Zhou
, J. Math. Phys.
39
, 2848
(1998
).30.
L. D.
Faddeev
and L. A.
Takhtajan
, Hamiltonian Methods in the Theory of Solitons
(Springer-Verlag
, 1987
).31.
Z. J.
Qiao
, Rev. Math. Phys.
13
, 545
(2001
).32.
V. I.
Arnold
, Mathematical Methods of Classical Mechanics
(Springer
, 1978
).33.
C. W.
Cao
and X. G.
Geng
, in Nonlinear Physics, Research Reports in Physics
, edited by C. H.
Gu
, Y. S.
Li
, and G. Z.
Tu
(Springer
, 1990
), p. 66
.34.
C. W.
Cao
, Y. T.
Wu
, and X. G.
Geng
, J. Math. Phys.
40
, 3948
(1999
).35.
R. G.
Zhou
, J. Math. Phys.
38
, 2535
(1997
).36.
Z. J.
Qiao
, Commun. Math. Phys.
239
, 309
(2003
).37.
X. G.
Geng
and H. H.
Dai
, Chaos, Solitons Fractals
20
, 311
(2004
).38.
B. Q.
Xia
, J. Math. Phys.
52
, 063506
(2011
).39.
40.
H. M.
Farkas
and I.
Kra
, Riemann Surfaces
, 2nd ed. (Springer
, 1992
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
