On Darboux integrable semi-discrete systems of exponential type

Abstract

In the present paper we consider a discretization of hyperbolic systems of exponential type. We proved that, in the case of $2\times 2$ systems, the resulting semi-discrete system is Darboux integrable only if it corresponds to a Cartan matrix of a semi-simple Lie algebra.

12 pages

References in corpus (1)

• On Some Algebraic Properties of Semi-Discrete Hyperbolic Type Equations