A. P. Fordy, A. B. Shabat, A. P. Veselov, “Factorization and Poisson correspondences”, TMF, 105:2 (1995), 225–245; Theoret. and Math. Phys., 105:2 (1995), 1369

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 105, Number 2, Pages 225–245 (Mi tmf1371)

This article is cited in 11 scientific papers (total in 12 papers)

Factorization and Poisson correspondences

A. P. Fordy^a, A. B. Shabat^b, A. P. Veselov^c

^a University of Leeds
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
^c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (1723 kB) Citations (12)

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Abstract: The Darboux transformation as an example of an integrable infinite-dimensional Poisson correspondence is discussed in the context of the general factorization problem. Generalizations related to energy dependent Schrödinger operators and to Kac–Moody algebras are considered. We also present the finite dimensional reductions of the Darboux transformation to stationary flows.

Received: 29.11.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 105, Issue 2, Pages 1369–1386
DOI: https://doi.org/10.1007/BF02070933

Bibliographic databases:

Language: Russian

Citation: A. P. Fordy, A. B. Shabat, A. P. Veselov, “Factorization and Poisson correspondences”, TMF, 105:2 (1995), 225–245; Theoret. and Math. Phys., 105:2 (1995), 1369–1386

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1371

https://www.mathnet.ru/eng/tmf/v105/i2/p225

This publication is cited in the following 12 articles:

Allan P Fordy, “Scaling symmetry reductions of coupled KdV systems”, J. Phys. A: Math. Theor., 57:45 (2024), 455205
Dianlou Du, Yuanyuan Lui, Xue Wang, “Integrable symplectic maps via reduction of Bäcklund transformation”, Theoret. and Math. Phys., 208:1 (2021), 886–895
V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1159–1176
J Mateo, J Negro, “Third-order differential ladder operators and supersymmetric quantum mechanics”, J. Phys. A: Math. Theor., 41:4 (2008), 045204
Andrew N. W. Hone, “Laurent Polynomials and Superintegrable Maps”, SIGMA, 3 (2007), 022, 18 pp.
A Sen, A N W Hone, P A Clarkson, “Darboux transformations and the symmetric fourth Painlevé equation”, J. Phys. A: Math. Gen., 38:45 (2005), 9751
Willox, R, “Painlevé equations from Darboux chains: I. P-III-P-V”, Journal of Physics A-Mathematical and General, 36:42 (2003), 10615
A N W Hone, V B Kuznetsov, O Ragnisco, “Bäcklund transformations for thesl(2) Gaudin magnet”, J. Phys. A: Math. Gen., 34:11 (2001), 2477
S. Janeczko, “Lagrangian submanifolds in product symplectic spaces”, Journal of Mathematical Physics, 41:8 (2000), 5642
A N W Hone, V B Kuznetsov, O Ragnisco, “Bäcklund transformations for many-body systems related to KdV”, J. Phys. A: Math. Gen., 32:27 (1999), L299
G.B. Byrnes, F.A. Haggar, G.R.W. Quispel, “Sufficient conditions for dynamical systems to have pre-symplectic or pre-implectic structures”, Physica A: Statistical Mechanics and its Applications, 272:1-2 (1999), 99
A. B. Borisov, S. A. Zykov, “The dressing chain of discrete symmetries and proliferation of nonlinear equations”, Theoret. and Math. Phys., 115:2 (1998), 530–541

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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