Characteristic Lie Algebra and Classification of Semi-Discrete Models

Abstract

Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.

33 pages, corrected typos, submitted to the Proceedings of the workshop "Nonlinear Physics: Theory and Experiment IV", Theoretical Mathematical Physics

References in corpus (7)

• Classification of integrable equations on quad-graphs. The consistency approach
• Discrete analogues of the Liouville equation
• Characteristic Algebras of Fully Discrete Hyperbolic Type Equations
• Characteristic Lie Algebra and Classification of Semi-Discrete Models
• On the Classification of Darboux Integrable Chains
• Variable Coefficient Third Order KdV Type of Equations
• On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations

Cited by in corpus (12)

• On Darboux integrability of discrete 2D Toda lattices
• On a classification algorithm of the integrable two-dimensional lattices via Lie-Rinehart algebras
• Characteristic Lie Algebra and Classification of Semi-Discrete Models
• On the Classification of Darboux Integrable Chains
• Complete list of Darboux Integrable Chains of the form $t_{1x}=t_x+d(t,t_1)$
• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
• On Darboux Integrable Semi-Discrete Chains
• Cartan matrices and integrable lattice Toda field equations
• Classification of integrable discrete Klein-Gordon models
• On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations
• Integral preserving discretization of 2D Toda lattices
• On existence of an x-integral for a semi-discrete chain of hyperbolic type