@article{TMF_2000_122_2_a5,
author = {G. Falqui and F. Magri and G. Tondo},
title = {Reduction of {bi-Hamiltonian} systems and separation of variables: {An} example from the {Boussinesq} hierarchy},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {212--230},
year = {2000},
volume = {122},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a5/}
}
TY - JOUR AU - G. Falqui AU - F. Magri AU - G. Tondo TI - Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 212 EP - 230 VL - 122 IS - 2 UR - http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a5/ LA - ru ID - TMF_2000_122_2_a5 ER -
%0 Journal Article %A G. Falqui %A F. Magri %A G. Tondo %T Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 212-230 %V 122 %N 2 %U http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a5/ %G ru %F TMF_2000_122_2_a5
G. Falqui; F. Magri; G. Tondo. Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 2, pp. 212-230. http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a5/
[1] F. Magri, T. Marsico, “Some developments of the concepts of Poisson manifolds in the sense of A. Lichnerowicz”, Gravitation, Electromagnetism, and Geometric Structures, ed. G. Ferrarese, Pitagora Editrice, Bologna, 1996, 207–222
[2] C. Morosi, G. Tondo, J. Phys. A, 30 (1997), 2799–2806 | DOI | MR | Zbl
[3] S. I. Alber, Commun. Pure Appl. Math., 34 (1981), 259–272 | DOI | MR | Zbl
[4] M. Antonowicz, A. P. Fordy, S. Wojciechowski, Phys. Lett. A, 124 (1987), 455–462 | DOI | MR
[5] O. I. Bogoyavlenskii, S. P. Novikov, Funkts. analiz i ego prilozh., 10:1 (1976), 9–13 | MR | Zbl
[6] B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “Integriruemye sistemy, I”, Dinamicheskie sistemy – 4, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, ed. R. V. Gamkrelidze, VINITI, M., 1985, 179–285 | MR
[7] I. M. Gel'fand, I. Zakharevich, “On the local geometry of a bi-Hamiltonian structure”, The Gelfand Mathematical Seminars 1990–1992, eds. L. Corwin et al., Birkhäuser, Boston, 1993, 51–112 | DOI | MR | Zbl
[8] P. Casati, G. Falqui, F. Magri, M. Pedroni, J. Math. Phys., 38 (1997), 4605–4628 | DOI | MR
[9] G. Falqui, F. Magri, M. Pedroni, Commun. Math. Phys., 197 (1998), 303–324 | DOI | MR | Zbl
[10] M. Sato, Y. Sato, “Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold”, Nonlinear PDEs in Applied Sciences, US-Japan Seminar (Tokyo), eds. P. Lax, H. Fujita, North-Holland Publ. Company, Amsterdam, 1982, 259–271 | MR
[11] L. A. Dickey, Soliton Equations and Hamiltonian Systems, Adv. Ser. in Math. Phys., 12, World Scientific, Singapore, 1991 | DOI | MR | Zbl
[12] F. Magri, C. Morosi, A geometric characterization of integrable Hamiltonian systems through the theory of Poisson–Nijenhuis manifolds, Quaderno S/19, Università di Milano, 1984
[13] A. G. Reiman, M. A. Semenov-Tyan-Shanskii, “Teoretiko-gruppovye metody v teorii integriruemykh sistem”, Dinamicheskie sistemy – 7, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 16, ed. R. V. Gamkrelidze, VINITI, M., 1987, 119–194 | MR | Zbl
[14] G. Magnano, F. Magri, Rev. Math. Phys., 3 (1991), 403–466 | DOI | MR | Zbl
[15] M. Pedroni, P. Vanhaecke, Reg. Chaotic Dyn., 3 (1998), 132–160 | DOI | MR | Zbl
[16] J. E. Marsden, T. Ratiu, Lett. Math. Phys., 11 (1986), 161–169 | DOI | MR | Zbl
[17] P. Casati, F. Magri, M. Pedroni, “Bihamiltonian manifolds and $\tau$-function”, Mathematical Aspects of Classical Field Theory, Contemp. Math., 132, eds. M. J. Gotay et al., American Mathematical Society, Providence, R.I., 1991, 213–234 | DOI | MR
[18] A. P. Fordy, S. D. Harris, “Hamiltonian structures in stationary manifold coordinates”, Algebraic Aspects of Integrable Systems, Progr. Nonlinear Differ. Equ. Appl., 26, eds. A. S. Fokas, I. M. Gelfand, Birkhauser, Boston, MA, 1996, 103–130 | MR
[19] A. Fokas, B. Fuchssteiner, Physica D, 4 (1981), 47–66 | DOI | MR | Zbl
[20] R. Brouzet, R. Caboz, J. Rabenivo, V. Ravoson, J. Phys. A, 29 (1996), 2069–2076 | DOI | MR | Zbl
[21] E. Sklyanin, Progr. Theor. Phys. Suppl., 118 (1995), 35–60 | DOI | MR | Zbl
[22] S. De Filippo, G. Marmo, M. Salerno, G. Vilasi, Nuovo Cimento B, 83 (1984), 97–112 | DOI | MR
[23] S. Benenti, “Separability structures on Riemannian manifolds”, Differential Geometrical Methods in Mathematical Physics, Lect. Notes Math., 836, eds. P. L. García, A. Péres-Rendón, and J. M. Sourian, Springer, Berlin, 1980, 512–538 | DOI | MR
[24] G. Tondo, J. Phys. A, 28 (1995), 5097–5115 | DOI | MR | Zbl
[25] T. Levi-Civita, Math. Annal., 59 (1904), 383–397 | DOI | MR | Zbl
[26] G. Tondo, “On the integrability of Hénon–Heiles type systems”, Non Linear Physics, Theory and Experiment, eds. E. Alfinito et al., World Scientific, Singapore, 1996, 313–320 | MR | Zbl
[27] M. Błaszak, Multi–Hamiltonian Theory of Dynamical Systems, Springer, Berlin, 1998 | MR
[28] C. Morosi, G. Tondo, Rep. Math. Phys. (to appear) | Zbl