An algebraic criterion of the Darboux integrability of differential-difference equations and systems
| Autor: | M. N. Kuznetsova, I. T. Habibullin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Pure mathematics Integrable system Nonlinear Sciences - Exactly Solvable and Integrable Systems General Physics and Astronomy Differential difference equations FOS: Physical sciences Statistical and Nonlinear Physics Type (model theory) System of linear equations Connection (mathematics) Set (abstract data type) Nonlinear Sciences::Exactly Solvable and Integrable Systems If and only if Modeling and Simulation Algebraic number Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics Mathematics |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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