Geodesic
Lax Pair for a Novel Two-Dimensional Lattice
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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In paper by I.T. Habibullin and our joint paper the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the characteristic Lie–Rinehart algebras. The method was applied for the classification of integrable cases of different subclasses of equations $u_{n,xy} = f(u_{n+1},u_n,u_{n-1}, u_{n,x},u_{n,y})$ of special forms. Under this approach the novel integrable chain was obtained. In present paper we construct Lax pair for the novel chain. To construct the Lax pair, we use the scheme suggested in papers by E.V. Ferapontov. We also study the periodic reduction of the chain.
Keywords: two-dimensional lattice, integrable reduction, characteristic algebra, Lie–Rinehart algebra, Darboux integrable system, higher symmetry, $x$-integral.
Mots-clés : Lax pair 
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     author = {Maria N. Kuznetsova},
     title = {Lax {Pair} for a {Novel} {Two-Dimensional} {Lattice}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a87/}
}
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Maria N. Kuznetsova. Lax Pair for a Novel Two-Dimensional Lattice. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a87/

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