V. E. Adler, A. B. Shabat, “Generalized Legendre transformations”, TMF, 112:2 (1997), 179–194; Theoret. and Math. Phys., 112:2 (1997), 935

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 112, Number 2, Pages 179–194
DOI: https://doi.org/10.4213/tmf1038 (Mi tmf1038)

This article is cited in 28 scientific papers (total in 28 papers)

Generalized Legendre transformations

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 (310 kB) Citations (28)

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DOI: https://doi.org/10.4213/tmf1038

Abstract: We discuss a general theory of the integrable Toda lattices which are considered as Lagrangian dynamical systems with one continuous and one discrete time. The invariance with respect to an analog of the classical Legendre transformations implies their integrability.

Received: 04.06.1997

English version:
Theoretical and Mathematical Physics, 1997, Volume 112, Issue 2, Pages 935–948
DOI: https://doi.org/10.1007/BF02634155

Bibliographic databases:

Language: Russian

Citation: V. E. Adler, A. B. Shabat, “Generalized Legendre transformations”, TMF, 112:2 (1997), 179–194; Theoret. and Math. Phys., 112:2 (1997), 935–948

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1038

https://doi.org/10.4213/tmf1038

https://www.mathnet.ru/eng/tmf/v112/i2/p179

This publication is cited in the following 28 articles:

Zhao X., Li Yu., Wang H., “Manifold Based on Neighbour Mapping and Its Projection For Remote Sensing Image Segmentation”, Int. J. Remote Sens., 40:24 (2019), 9304–9320
Suris Yu.B., “Discrete Time Toda Systems”, J. Phys. A-Math. Theor., 51:33 (2018)
Adler V.E., “Integrability Test For Evolutionary Lattice Equations of Higher Order”, J. Symbolic Comput., 74 (2016), 125–139
Zhang Yu., Zhou R.-G., “A Chain of Type II and Its Exact Solutions”, Chin. Phys. Lett., 33:11 (2016), 110203
V. G. Marikhin, “Action as an invariant of Bäcklund transformations for Lagrangian systems”, Theoret. and Math. Phys., 184:1 (2015), 953–960
Raphael Boll, Matteo Petrera, Yuri B Suris, “Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems”, J. Phys. A: Math. Theor., 48:8 (2015), 085203
Atkinson J., Joshi N., “Singular-Boundary Reductions of Type-Q Abs Equations”, Int. Math. Res. Notices, 2013, no. 7, 1451–1481
Perez Teruel G.R., “An Alternative Formulation of Classical Mechanics Based on an Analogy with Thermodynamics”, Eur. J. Phys., 34:6 (2013), 1589–1599
Boll R., Suris Yu.B., “Non-symmetric discrete Toda systems from quad-graphs”, Appl Anal, 89:4 (2010), 547–569
A. Shabat, Lecture Notes in Physics, 767, Integrability, 2009, 139
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
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
I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510
V. E. Adler, V. G. Marikhin, A. B. Shabat, “Lagrangian Chains and Canonical Bäcklund Transformations”, Theoret. and Math. Phys., 129:2 (2001), 1448–1465
V. E. Adler, “Discretizations of the Landau–Lifshits equation”, Theoret. and Math. Phys., 124:1 (2000), 897–908
V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
V. E. Adler, “Legendre Transforms on a Triangular Lattice”, Funct. Anal. Appl., 34:1 (2000), 1–9

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

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