Integrability of dynamical systems and the singular-point analysis

1985 ◽  
Vol 15 (6) ◽  
pp. 637-666 ◽  
Author(s):  
W. -H. Steeb ◽  
M. Kloke ◽  
B. M. Spieker ◽  
A. Kunick

1986 ◽  
Vol 33 (3) ◽  
pp. 2131-2133 ◽  
Author(s):  
W.-H. Steeb ◽  
J. A. Louw ◽  
P. G. L. Leach ◽  
F. M. Mahomed


1987 ◽  
Vol 20 (12) ◽  
pp. 4027-4030 ◽  
Author(s):  
W -H Steeb ◽  
J A Louw ◽  
M F Maritz


2008 ◽  
Vol 86 (6) ◽  
pp. 783-789 ◽  
Author(s):  
J R Schmidt

The Gaudin equations, a set of conditions of integrability imposed on the coupling constants of a lattice spin model, are solved by singular point analysis and the Painleve’ test. The Gaudin equations are transformed into systems of differential equations. The subset that are similarity-invariant have two, one, or zero constants of the motion corresponding to elliptic, trigonometric and (or) hyperbolic, and rational solutions, respectively. All solutions can be found at least formally by this technique. All similarity-invariant solutions are odd functions. There exist solutions with regular, even parts whose squares sum to a constant.PACS Nos.: 02.30.Ik, 02.40.Xx, 03.65.Fd



1991 ◽  
Vol 152 (7) ◽  
pp. 339-342 ◽  
Author(s):  
W.-H. Steeb ◽  
W.D. Heiss


1984 ◽  
Vol 39 (17) ◽  
pp. 429-432 ◽  
Author(s):  
W.-H. Steeb ◽  
M. Kloke ◽  
B. M. Spieker ◽  
A. Grauel


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