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TMF, 2008, Volume 155, Number 2, Pages 344–355 (Mi tmf6216)  

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

Symmetries of nonlinear hyperbolic systems of the Toda chain type

V. V. Sokolova, S. Ya. Startsevb

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

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

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

Full text: PDF file (400 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 155:2, 802–811

Bibliographic databases:

Received: 30.06.2007

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Habibullin I., Zheltukhina N., Pekcan A., “On the classification of Darboux integrable chains”, J. Math. Phys., 49:10 (2008), 102702, 39 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. 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.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. D. K. Demskoi, “Integrals of open two-dimensional lattices”, Theoret. and Math. Phys., 163:1 (2010), 466–471  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    5. 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  crossref  isi  scopus
    6. Startsev S.Ya., “Darboux Integrable Discrete Equations Possessing An Autonomous First-Order Integral”, J. Phys. A-Math. Theor., 47:10 (2014), 105204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, Theoret. and Math. Phys., 182:2 (2015), 189–210  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. 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.  mathnet  crossref
    9. Startsev S.Ya., “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01  crossref  mathscinet  zmath  isi  scopus
    10. A. B. Shabat, V. E. Adler, “Cartan matrices in the Toda–Darboux chain theory”, Theoret. and Math. Phys., 196:1 (2018), 957–964  mathnet  crossref  crossref  adsnasa  isi  elib
    11. 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  mathnet  crossref  isi
    12. S. Ya. Startsev, “Draivery simmetrii i formalnye integraly giperbolicheskikh sistem uravnenii”, Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 152, VINITI RAN, M., 2018, 110–119  mathnet  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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