English

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

Exactly Solvable and Integrable Systems 2021-12-06 v2

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.

Keywords

Cite

@article{arxiv.2106.08577,
  title  = {An algebraic criterion of the Darboux integrability of differential-difference equations and systems},
  author = {I. T. Habibullin and M. N. Kuznetsova},
  journal= {arXiv preprint arXiv:2106.08577},
  year   = {2021}
}

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21 pages