Lax Pair for a Novel Two-Dimensional Lattice

Abstract

In the paper by I.T. Habibullin and our joint paper, the algorithm for the 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 𝑢ₙ‚ₓy = 𝑓(𝑢ₙ₊₁, 𝑢ₙ, 𝑢ₙ₋₁, 𝑢ₙ‚ₓ, 𝑢ₙ,y) of special forms. Under this approach, the novel integrable chain was obtained. In the present paper, we construct a 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.