On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations
Ismagil Habibullin, Asli Pekcan, Natalya Zheltukhina
TL;DR
This paper investigates algebraic properties of nonlinear semi-discrete hyperbolic equations, focusing on Darboux integrability and its application to classifying integrable chains, advancing understanding of their algebraic structure.
Contribution
It provides an algebraic formulation of Darboux integrability for semi-discrete equations and explores its use in classifying integrable chains.
Findings
Algebraic formulation of Darboux integrability for semi-discrete equations
Approach to classify Darboux integrable chains
Insights into algebraic structures of hyperbolic type equations
Abstract
Nonlinear semi-discrete equations of the form t_x(n+1)=f(t(n), t(n+1), t_x(n)) are studied. An adequate algebraic formulation of the Darboux integrability is discussed and the attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.
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Taxonomy
TopicsNonlinear Waves and Solitons · Differential Equations and Numerical Methods · Numerical methods for differential equations