Lax Pair for a Novel Two-Dimensional Lattice

In paper by I.T. Habibullin and our joint the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on requirement existence an infinite set Darboux reductions notion characteristic Lie-Rinehart algebras. The applied cases different subclasses $u_{n,xy} = f(u_{n+1},u_n,u_{n-1}, u_{n,x},u_{n,y})$ special forms. Under this approach novel chain obtained. present we construct Lax pair chain. To pair, use scheme suggested in papers E.V. Ferapontov. We also study periodic reduction