Solvable and/or integrable and/or linearizable N-Body problems in ordinary (three-dimensional) space. I

Journal of Nonlinear Mathematical Physics

Volumn 7, Issue 3, 2000, Pages 303-385

  Bruschi, M ^a   Calogero, F ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034552814     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2000.7.3.4     Document Type: Article

References (11)

1. Calogero, F., 1996. A Solvable n-Body Problem in the Plane. I. J. Math. Phys., 37:1735–1759. Three Solvable Many-Body Problems in the Plane, Acta Applicandae Mathematicae, 1998, V.51, 93–111; Tricks of the Trade:Relating and Deriving Solvable and Integrable Dynamical Systems, Calogero-Moser-Sutherland Models I, in Proceedings of the Workshop on Calogero-Moser-Sutherland Models, Montreal, 10–15 March 1997, Editors van Diejen and L. Vinet, Springer, 2000, 93–116; Integrable and Solvable Many-Body Problems in the Plane via Complexification, J. Math. Phys., 1988, V.39, 5268–5291; A Solvable Many-Body Problem in the Plane, J. Nonlinear Math. Phys., 1998, V.5, 289–293
2. Calogero, F., 1993. Interpolation in Multidimensions, a Convenient Finite-Dimensional Matrix Representation of the (Partial) Differential Operators, and some Applications. J. Math. Phys., 34:4704–4724. (b) Calogero F., Xiaoda Ji, Solvable (Nonrelativistic, Classical) n-Body Problems in Multidimensions. I, J. Math. Phys., 1994, V.35, 710–733; (c) Solvable (Nonrelativistic, Classical) n-Body Problems in Multidimensions. II, in National Workshop on Nonlinear Dynamics, Editors M. Costato, A. Degasperis and M. Milani, Conference Proceedings vol. 48, Società Italiana di Fisica, Bologna, 1995, 21–32
3. Golubchik, I.Z., and Sokolov, V.V., 1997. On Some Generalizations of the Factorization Method. Theor. Math. Phys., 110:267–276. (Russian version:Teor. Mat. Fyz., 1997, V.110, 339–350)
4. Bruschi, M., Manakov, S.V., Ragnisco, O., and Levi, D., 1980. The Nonabelian Toda Lattice–Discrete Analogue of the Matrix Schroedinger Spectral Problem. J. Math. Phys., 21:2749–2753.
5. Bruschi, M., Ragnisco, O., and Levi, D., 1981. Evolution Equations Associated with the Discrete Analog of the Matrix Schroedinger Spectral Problem Solvable via the Inverse Spectral Transform. J. Math. Phys., 22:2463–2471.
6. Bruschi, M., and Ragnisco, O., 1983. On the Inversion of the Commutation Operator. Lett. Nuovo Cimento, 38:41–44. (There is a misprint in formula (7) of this paper, which should read
7. Nahm, W., 1982. The Algebraic Geometry of Multipoles, in Group Theoretical Methods in Physics, Edited by:Serdaroglu, M., and Inonu, E., Vol. 180, 456–466. Springer. Lecture Notes in Physics
8. Adler, V.E., and Shabat, A.B., 1997. Generalized Legendre Transformations. Theor. Math. Phys., 112:935–948. (Russian version:Teor. Mat. Fys., 1997, V.112, 179–194)
9. Svinolupov, S.I., and Sokolov, V.V., 1996. Deformations of Triple-Jordan Systems and Integrable Equations. Theor. Math. Phys., 108:1160–1163. (Russian version:Teor. Mat. Fyz., 1996, V.108, 388–392)
10. Gradshteyn, I.D., and Ryzhik, I.M., 1994. Table of Integrals, Series, and Products, London:Academic Press.
11. Levi, D., Ragnisco, O., and Bruschi, M., 1983. Continuous and Discrete Matrix Burger’s Hierarchies. Nuovo Cimento, 74B:33–51.