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

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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 3, Pages 401–421
DOI: https://doi.org/10.4213/tmf28 (Mi tmf28)

This article is cited in 20 scientific papers (total in 20 papers)

Laplace Invariants of Two-Dimensional Open Toda Lattices

A. M. Gurieva^a, A. V. Zhiber^b

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

Full-text PDF (297 kB) Citations (20)

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

Abstract: We show that Toda lattices with the Cartan matrices

A_{n}

$\mathrm{A}_{n}$ ,

B_{n}

$\mathrm{B}_{n}$ ,

C_{n}

$\mathrm{C}_{n}$ и

D_{n}

$\mathrm{D}_{n}$ 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

$x$ and

y

$y$ integrals) and higher symmetries.

Keywords: symmetries, integrals, Laplace invariants, generalized invariants.

Received: 24.03.2003

English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 3, Pages 338–355
DOI: https://doi.org/10.1023/B:TAMP.0000018451.74151.34

Bibliographic databases:

Language: Russian

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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https://doi.org/10.4213/tmf28

https://www.mathnet.ru/eng/tmf/v138/i3/p401

This publication is cited in the following 20 articles:

I. V. Rakhmelevich, “Ob invariantakh Laplasa dvumernykh nelineinykh uravnenii vtorogo poryadka s odnorodnym polinomom”, Izv. vuzov. Matem., 2024, no. 8, 55–64
I.T. Habibullin, A.U. Sakieva, “On integrable reductions of two-dimensional Toda-type lattices”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100854
I. V. Rakhmelevich, “On Laplace Invariants of Two-Dimensional Nonlinear Equations of the Second Order with Homogeneous Polynomial”, Russ Math., 68:8 (2024), 47
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
Athorne Ch., Yilmaz H., “Invariants of Hyperbolic Partial Differential Operators”, J. Phys. A-Math. Theor., 49:13 (2016), 135201
Demskoi D.K. Tran D.T., “Darboux integrability of determinant and equations for principal minors”, Nonlinearity, 29:7 (2016), 1973–1991
S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, Theoret. and Math. Phys., 182:2 (2015), 189–210
Nie Zh., “On Characteristic Integrals of Toda Field Theories”, J. Nonlinear Math. Phys., 21:1 (2014), 120–131
Athorne Ch. Yilmaz H., “Laplace Invariants for General Hyperbolic Systems”, J. Nonlinear Math. Phys., 19:3 (2012), 1250024
Voronova Yu.G., “O zadache koshi dlya odnoi lineinoi giperbolicheskoi sistemy uravnenii”, Izvestiya Ufimskogo nauchnogo tsentra RAN, 2012, no. 2, 5–9 The cauchy problem for a linear hyperbolic system of equations
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
Yu. G. Voronova, “O zadache Koshi dlya lineinykh giperbolicheskikh sistem uravnenii s nulevymi obobschennymi invariantami Laplasa”, Ufimsk. matem. zhurn., 2:2 (2010), 20–26
V. L. Vereshchagin, “Discrete Toda lattices and the Laplace method”, Theoret. and Math. Phys., 160:3 (2009), 1229–1237
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
Demskoi, DK, “On non-Abelian Toda A(2)((1)) model and related hierarchies”, Journal of Mathematical Physics, 50:12 (2009), 123516
S. Ya. Startsev, “Cascade Method of Laplace Integration for Linear Hyperbolic Systems of Equations”, Math. Notes, 83:1 (2008), 97–106
V. L. Vereshchagin, “Darboux-integrable discrete systems”, Theoret. and Math. Phys., 156:2 (2008), 1142–1153
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
S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253

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

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