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 an attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.
HABIBULLIN, İSMAGİL; PEKCAN, ASLI; and ZHELTUKHINA, NATALYA (2008) "On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations," Turkish Journal of Mathematics: Vol. 32: No. 3, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol32/iss3/3