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

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.

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

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Cited by in corpus (6)

• Characteristic Lie Algebras of Integrable Differential-Difference Equations in 3D
• On a class of 2D integrable lattice equations
• Construction of exact solutions of nonlinear PDE via dressing chain in 3D
• Integral preserving discretization of 2D Toda lattices
• Integrability conditions for two-dimensional lattices
• An algebraic criterion of the Darboux integrability of differential-difference equations and systems