V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, TMF, 155:2 (2008), 344–355; Theoret. and Math. Phys., 155:2 (2008), 802

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 2, Pages 344–355
DOI: https://doi.org/10.4213/tmf6216 (Mi tmf6216)

This article is cited in 14 scientific papers (total in 14 papers)

Symmetries of nonlinear hyperbolic systems of the Toda chain type

V. V. Sokolov^a, S. Ya. Startsev^b

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

Full-text PDF (400 kB) Citations (14)

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DOI: https://doi.org/10.4213/tmf6216

Abstract: We consider hyperbolic systems of equations that have full sets of integrals along both characteristics. The best known example of models of this type is given by two-dimensional open Toda chains. For systems that have integrals, we construct a differential operator that takes integrals into symmetries. For systems of the chosen type, this proves the existence of higher symmetries dependent on arbitrary functions.

Keywords: Liouville equation, Toda chain, integral, higher symmetry, hyperbolic system of partial differential equations, Noether theorem.

Received: 30.06.2007

English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 2, Pages 802–811
DOI: https://doi.org/10.1007/s11232-008-0069-9

Bibliographic databases:

Language: Russian

Citation: V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, TMF, 155:2 (2008), 344–355; Theoret. and Math. Phys., 155:2 (2008), 802–811

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This publication is cited in the following 14 articles:

S Ya Startsev, “Darboux integrability of hyperbolic partial differential equations: is it a property of integrals rather than equations?”, J. Phys. A: Math. Theor., 58:2 (2025), 025206
Sergey V Smirnov, “Integral preserving discretization of 2D Toda lattices”, J. Phys. A: Math. Theor., 56:26 (2023), 265204
A. B. Shabat, V. E. Adler, “Cartan matrices in the Toda–Darboux chain theory”, Theoret. and Math. Phys., 196:1 (2018), 957–964
S. Ya. Startsev, “Structure of set of symmetries for hyperbolic systems of Liouville type and generalized Laplace invariants”, Ufa Math. J., 10:4 (2018), 103–110
S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, J. Math. Sci. (N. Y.), 252:2 (2021), 232–241
Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.
Startsev S.Ya., “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01
S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, Theoret. and Math. Phys., 182:2 (2015), 189–210
Startsev S.Ya., “Darboux Integrable Discrete Equations Possessing An Autonomous First-Order Integral”, J. Phys. A-Math. Theor., 47:10 (2014), 105204
Kiselev A.V., “Homological Evolutionary Vector Fields in Korteweg-de Vries, Liouville, Maxwell, and Several Other Models”, 7th International Conference on Quantum Theory and Symmetries (QTS7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012058
A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162
D. K. Demskoi, “Integrals of open two-dimensional lattices”, Theoret. and Math. Phys., 163:1 (2010), 466–471
Demskoi D.K., Lee Jyh-Hao, “On non-Abelian Toda $A_2^{(1)}$ model and related hierarchies”, J. Math. Phys., 50:12 (2009), 123516, 11 pp.
Habibullin I., Zheltukhina N., Pekcan A., “On the classification of Darboux integrable chains”, J. Math. Phys., 49:10 (2008), 102702, 39 pp.

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

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