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arXiv · 2106.08577

An algebraic criterion of the Darboux integrability of differential-difference equations and systems

I. T. Habibullin·M. N. Kuznetsova
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Abstract

The article investigates systems of differential-difference equations of hyperbolic type, integrable in sense of Darboux. The concept of a complete set of independent characteristic integrals underlying Darboux integrability is discussed. A close connection is found between integrals and characteristic Lie-Rinehart algebras of the system. It is proved that a system of equations is Darboux integrable if and only if its characteristic algebras in both directions are finite-dimensional.

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I. T. Habibullin, M. N. Kuznetsova. 2021-06-16. An algebraic criterion of the Darboux integrability of differential-difference equations and systems. https://doi.org/10.1088/1751-8121%2Fac37e8

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