V. E. Adler, A. B. Shabat, “On the one class of the Toda chains”, TMF, 111:3 (1997), 323–334; Theoret. and Math. Phys., 111:3 (1997), 647

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 111, Number 3, Pages 323–334
DOI: https://doi.org/10.4213/tmf1011 (Mi tmf1011)

This article is cited in 27 scientific papers (total in 27 papers)

On the one class of the Toda chains

V. E. Adler^a, A. B. Shabat^b

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (240 kB) Citations (27)

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DOI: https://doi.org/10.4213/tmf1011

Abstract: The main result of our paper is the list of integrable generalizations of the Toda lattice. Apart from known lattices this list contains three new examples. Each lattice from the list gives the Bäcklund transformation for some NLS type system.

Received: 04.03.1997

English version:
Theoretical and Mathematical Physics, 1997, Volume 111, Issue 3, Pages 647–657
DOI: https://doi.org/10.1007/BF02634053

Bibliographic databases:

Language: Russian

Citation: V. E. Adler, A. B. Shabat, “On the one class of the Toda chains”, TMF, 111:3 (1997), 323–334; Theoret. and Math. Phys., 111:3 (1997), 647–657

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Linking options:

https://www.mathnet.ru/eng/tmf1011

https://doi.org/10.4213/tmf1011

https://www.mathnet.ru/eng/tmf/v111/i3/p323

This publication is cited in the following 27 articles:

Suris Yu.B., “Discrete Time Toda Systems”, J. Phys. A-Math. Theor., 51:33 (2018)
Aminov G., Mironov A., Morozov A., “Modular Properties of 6D (Dell) Systems”, J. High Energy Phys., 2017, no. 11, 023
V. G. Marikhin, “Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system”, Theoret. and Math. Phys., 189:3 (2016), 1718–1725
Zhang Yu. Zhou R.-G., “A Chain of Type II and Its Exact Solutions”, Chin. Phys. Lett., 33:11 (2016), 110203
Boll R., Petrera M., Suris Yu.B., “Multi-Time Lagrangian 1-Forms For Families of Backlund Transformations. Relativistic Toda-Type Systems”, J. Phys. A-Math. Theor., 48:8 (2015), 085203
Chen Ya., Ismail M.E.H., “Hypergeometric Origins of Diophantine Properties Associated with the Askey Scheme”, Proceedings of the American Mathematical Society, 138:3 (2010), 943–951
R. I. Yamilov, “Integrability conditions for an analogue of the relativistic Toda chain”, Theoret. and Math. Phys., 151:1 (2007), 492–504
Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.
Yamilov, R, “Symmetries as integrability criteria for differential difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), R541
R. I. Yamilov, “Relativistic Toda Chains and Schlesinger Transformations”, Theoret. and Math. Phys., 139:2 (2004), 623–635
Adler, VE, “Q(4): Integrable master equation related to an elliptic curve”, International Mathematics Research Notices, 2004, no. 47, 2523
Ustinov, NV, “The lattice equations of the Toda type with an interaction between a few neighbourhoods”, Journal of Physics A-Mathematical and General, 37:5 (2004), 1737
Suris Y.B., “Discrete Lagrangian models”, Discrete Integrable Systems, Lecture Notes in Physics, 644, 2004, 111–184
S. D. Vereshchagin, A. V. Yurov, “The Darboux Transformation and Exactly Solvable Cosmological Models”, Theoret. and Math. Phys., 139:3 (2004), 787–800
Cieslinski, JL, “Darboux covariant equations of von Neumann type and their generalizations”, Journal of Mathematical Physics, 44:4 (2003), 1763
A. K. Svinin, “Integrable Chains and Hierarchies of Differential Evolution Equations”, Theoret. and Math. Phys., 130:1 (2002), 11–24
A. Gorsky, A. Mironov, Integrable Hierarchies and Modern Physical Theories, 2001, 33
V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
A. B. Shabat, “Third version of the dressing method”, Theoret. and Math. Phys., 121:1 (1999), 1397–1408
Marikhin V.G., Shabat A.B., “Hamiltonian theory of Backlund transformations”, Optical Solitons: Theoretical Challenges and Industrial Perspectives, Centre de Physique Des Houches, no. 12, 1999, 19–29

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

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