An algebraic criterion of the Darboux integrability of differential-difference equations and systems
arXiv:2106.08577 · doi:10.1088/1751-8121/ac37e8
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.
21 pages
References in corpus (6)
- On a classification algorithm of the integrable two-dimensional lattices via Lie-Rinehart algebras
- Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings
- Characteristic Lie Algebras of Integrable Differential-Difference Equations in 3D
- On Darboux Integrable Semi-Discrete Chains
- On a class of 2D integrable lattice equations
- Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations