On a classification algorithm of the integrable two-dimensional lattices via Lie-Rinehart algebras

2019/07/29 by I. T. Habibullin, М. Н. Кузнецова, M. N. Kuznetsova · 3 citations
Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.1134/s0040577920040121

IX-th International Conference "SOLITONS, COLLAPSES AND TURBULENCE: Achievements, Developments and Perspectives (SCT-19)'' in honor of Vladimir Zakharov's 80th birthday

arxiv created 2019/07/29 · crossref issued 2020/04/01 · crossref published 2020/04/01 · crossref published-print 2020/04/01 · openalex publication_date 2020/04/01 · crossref published-online 2020/04/30 · crossref created 2020/04/30 · arxiv updated 2020/05/20 · openalex created_date 2025/10/10 · crossref deposited 2026/04/06 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31

Abstract

In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic equations of arbitrarily high order integrable in the Darboux sense. Darboux integrablity admits a remarkable algebraic interpretation: the Lie-Rinehart algebras related to both characteristic directions corresponding to the reduced system of the hyperbolic equations have to be of finite dimension. A classification algorithm based on the properties of the characteristic algebra is discussed. Some classification results are presented.

Citations

• Commutator identities on associative algebras and the integrability of nonlinear evolution equations
• Laplace transformations of hydrodynamic-type systems in Riemann invariants

Cited by

• Discrete integrable equations with three independent variables
• On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries
• Characteristic Lie algebras of integrable differential-difference equations in 3D

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