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TMF, 2004, Volume 138, Number 3, Pages 401–421 (Mi tmf28)  

This article is cited in 17 scientific papers (total in 17 papers)

Laplace Invariants of Two-Dimensional Open Toda Lattices

A. M. Gurievaa, A. V. Zhiberb

a Ufa State Aviation Technical University
b Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences

Abstract: We show that Toda lattices with the Cartan matrices $\mathrm{A}_{n}$, $\mathrm{B}_{n}$, $\mathrm{C}_{n}$ и $\mathrm{D}_{n}$ are Liouville-type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants. We show how they can be used to construct conservation laws ($x$ and $y$ integrals) and higher symmetries.

Keywords: symmetries, integrals, Laplace invariants, generalized invariants

DOI: https://doi.org/10.4213/tmf28

Full text: PDF file (297 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 138:3, 338–355

Bibliographic databases:

Received: 24.03.2003

Citation: A. M. Gurieva, A. V. Zhiber, “Laplace Invariants of Two-Dimensional Open Toda Lattices”, TMF, 138:3 (2004), 401–421; Theoret. and Math. Phys., 138:3 (2004), 338–355

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253  mathnet  crossref  mathscinet  zmath  elib  elib
    2. A. V. Zhiber, Yu. G. Mikhailova, “On hyperbolic systems of equations with zero generalized Laplace invariants”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S154–S164  mathnet  crossref  elib
    3. S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. V. L. Vereshchagin, “Darboux-integrable discrete systems”, Theoret. and Math. Phys., 156:2 (2008), 1142–1153  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. L. Vereshchagin, “Discrete Toda lattices and the Laplace method”, Theoret. and Math. Phys., 160:3 (2009), 1229–1237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. V. Zhiber, Yu. G. Mikhailova, “Algoritm postroeniya obschego resheniya $n$-komponentnoi giperbolicheskoi sistemy uravnenii s nulevymi invariantami Laplasa i kraevye zadachi”, Ufimsk. matem. zhurn., 1:3 (2009), 28–45  mathnet  zmath  elib
    7. Demskoi, DK, “On non-Abelian Toda A(2)((1)) model and related hierarchies”, Journal of Mathematical Physics, 50:12 (2009), 123516  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. 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
    9. 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
    10. Yu. G. Voronova, “O zadache Koshi dlya lineinykh giperbolicheskikh sistem uravnenii s nulevymi obobschennymi invariantami Laplasa”, Ufimsk. matem. zhurn., 2:2 (2010), 20–26  mathnet  zmath  elib
    11. Athorne Ch. Yilmaz H., “Laplace Invariants for General Hyperbolic Systems”, J. Nonlinear Math. Phys., 19:3 (2012), 1250024  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Voronova Yu.G., “O zadache koshi dlya odnoi lineinoi giperbolicheskoi sistemy uravnenii”, Izvestiya Ufimskogo nauchnogo tsentra RAN, 2012, no. 2, 5–9  elib
    13. Nie Zh., “On Characteristic Integrals of Toda Field Theories”, J. Nonlinear Math. Phys., 21:1 (2014), 120–131  crossref  mathscinet  isi  scopus  scopus
    14. 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
    15. Athorne Ch., Yilmaz H., “Invariants of Hyperbolic Partial Differential Operators”, J. Phys. A-Math. Theor., 49:13 (2016), 135201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. Demskoi D.K. Tran D.T., “Darboux integrability of determinant and equations for principal minors”, Nonlinearity, 29:7 (2016), 1973–1991  crossref  mathscinet  zmath  isi  elib  scopus
    17. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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