A classification algorithm for integrable two-dimensional lattices via Lie—Rinehart algebras

• Published in: Theoretical and mathematical physics Vol. 203; no. 1; pp. 569 - 581
• Main Authors: Habibullin, I. T., Kuznetsova, M. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2020; Springer Nature B.V
• Subjects: Algebra; Algorithms; Applications of Mathematics; Classification; Continuity (mathematics); Lattices (mathematics); Mathematical analysis; Mathematical and Computational Physics; Physics; Physics and Astronomy; Theoretical; cutoff condition; integrable reduction; characteristic Lie algebra; open lattice; Darboux-integrable system; two-dimensional integrable lattice; x-integral

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 sens...