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This article is cited in 16 scientific papers (total in 16 papers)
A classification algorithm for integrable two-dimensional lattices
via Lie–Rinehart algebras
I. T. Habibullinab, M. N. Kuznetsovaa a Institute of Mathematics with Computing Centre — Subdivision
of the Ufa Federal Research Centre of the~Russian Academy of Science, Ufa,
Russia
b Bashkir State University, Ufa, Russia
Abstract:
We study the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables. By integrability, we mean the presence of reductions of a chain to a system of hyperbolic equations of an arbitrarily high order that are integrable in the Darboux sense. Darboux integrability admits a remarkable algebraic interpretation: the Lie–Rinehart algebras related to both characteristic directions corresponding to the reduced system of hyperbolic equations must have a finite dimension. We discuss a classification algorithm based on the properties of the characteristic algebra and present some classification results. We find new examples of integrable equations.
Keywords:
two-dimensional integrable lattice, $x$-integral, integrable reduction,
cutoff condition, open lattice, Darboux-integrable system,
characteristic Lie algebra.
Received: 29.07.2019 Revised: 22.10.2019
Citation:
I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices
via Lie–Rinehart algebras”, TMF, 203:1 (2020), 161–173; Theoret. and Math. Phys., 203:1 (2020), 569–581
Linking options:
https://www.mathnet.ru/eng/tmf9786https://doi.org/10.4213/tmf9786 https://www.mathnet.ru/eng/tmf/v203/i1/p161
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