On Darboux integrable semi-discrete systems of exponential type

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.

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Zheltukhin, Kostyantyn, Bilen, Ergun
Format: Article
Language:English
Subjects:
Discrete systems
Hyperbolic systems
Lie groups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422