Abstract:
We prove the Darboux integrability of semidiscrete and discrete two-dimensional Toda lattices corresponding to simple Lie algebras of the A and C series.
Keywords:
discrete Toda lattice, discrete exponential system, Darboux integrability, integral along characteristics.
Citation:
S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, TMF, 182:2 (2015), 231–255; Theoret. and Math. Phys., 182:2 (2015), 189–210
This publication is cited in the following 22 articles:
I.T. Habibullin, A.U. Sakieva, “On integrable reductions of two-dimensional Toda-type lattices”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100854
M. N. Kuznetsova, I. T. Habibullin, A. R. Khakimova, “On the problem of classifying integrable chains with three independent variables”, Theoret. and Math. Phys., 215:2 (2023), 667–690
M. N. Kuznetsova, “Construction of localized particular solutions of chains with three independent variables”, Theoret. and Math. Phys., 216:2 (2023), 1158–1167
I. T. Habibullin, A. R. Khakimova, “On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras”, Theoret. and Math. Phys., 217:1 (2023), 1541–1573
Sergey V Smirnov, “Integral preserving discretization of 2D Toda lattices”, J. Phys. A: Math. Theor., 56:26 (2023), 265204
Ismagil T. Habibullin, Aigul R. Khakimova, Alfya U. Sakieva, “Miura-Type Transformations for Integrable Lattices in 3D”, Mathematics, 11:16 (2023), 3522
I. T. Habibullin, A. R. Khakimova, “Integrals and characteristic algebras for systems of discrete equations on a quadrilateral graph”, Theoret. and Math. Phys., 213:2 (2022), 1589–1612
I. T. Habibullin, A. R. Khakimova, “Algebraic reductions of discrete equations of Hirota-Miwa type”, Ufa Math. J., 14:4 (2022), 113–126
D. V. Millionshchikov, S. V. Smirnov, “Characteristic algebras and integrable exponential systems”, Ufa Math. J., 13:2 (2021), 41–69
Habibullin I.T. Kuznetsova M.N., “An Algebraic Criterion of the Darboux Integrability of Differential-Difference Equations and Systems”, J. Phys. A-Math. Theor., 54:50 (2021), 505201
Habibullin I.T. Khakimova A.R., “Characteristic Lie Algebras of Integrable Differential-Difference Equations in 3D”, J. Phys. A-Math. Theor., 54:29 (2021), 295202
I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices
via Lie–Rinehart algebras”, Theoret. and Math. Phys., 203:1 (2020), 569–581
I. T. Habibullin, M. N. Kuznetsova, A. U. Sakieva, “Integrability conditions for two-dimensional Toda-like equations”, J. Phys. A-Math. Theor., 53:39 (2020), 395203
I. Habibullin, A. Khakimova, “Integrable boundary conditions for the Hirota-Miwa equation and lie algebras”, J. Nonlinear Math. Phys., 27:3 (2020), 393–413
S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636
Ch. Athorne, H. Yilmaz, “Twisted Laplace maps”, J. Phys. A-Math. Theor., 52:22 (2019), 225201
I. T. Habibullin, A. R. Khakimova, “Discrete exponential type systems on a quad graph, corresponding to the affine lie algebras a(n)(-1)((1) )”, J. Phys. A-Math. Theor., 52:36 (2019), 365202
W. Fu, “Direct linearisation of the discrete-time two-dimensional Toda lattices”, J. Phys. A-Math. Theor., 51:33 (2018), 334001
M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105
Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 073, 26 pp.
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