An algebraic criterion of the Darboux integrability of differential-difference equations and systems-Reference-Cited by-同舟云学术

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

Published:2021-11-25 Issue:50 Volume:54 Page:505201
ISSN:1751-8113
Container-title:Journal of Physics A: Mathematical and Theoretical
language:
Short-container-title:J. Phys. A: Math. Theor.

Author:

Habibullin I T^ORCID,Kuznetsova M N^ORCID

Abstract

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.

Publisher

IOP Publishing

Subject

General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://iopscience.iop.org/article/10.1088/1751-8121/ac37e8/pdf

Reference30 articles.

1. Exactly integrable hyperbolic equations of Liouville type;Zhiber;Russ. Math. Surv.,2001

2. Recherches sur quelques équations aux dérivées partielles du second ordre;Goursat;Ann. Fac. Sci. Toulouse Math.,1899

3. Recherches sur quelques équations aux dérivées partielles du second ordre;Goursat;Ann. Fac. Sci. Toulouse Math.,1899

4. Sur les équations aux dérivées partialles du second order, F(x, y, p, q, r, s, t) = 0, inteqrables par la methode de Darboux;Vessiot;J. Math. Pures Appl.,1939

5. Sur les équations aux dérivées partialles du second order, F(x, y, p, q, r, s, t) = 0, integrables par la methode de Darboux;Vessiot;J. Math. Pures Appl.,1942

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Construction of Darboux integrable discrete models;Reports on Mathematical Physics;2023-12

2. Construction of localized particular solutions of chains with three independent variables;Teoreticheskaya i Matematicheskaya Fizika;2023-08

3. Construction of localized particular solutions of chains with three independent variables;Theoretical and Mathematical Physics;2023-08

4. Integral preserving discretization of 2D Toda lattices;Journal of Physics A: Mathematical and Theoretical;2023-06-09

5. Integrals and characteristic algebras for systems of discrete equations on a quadrilateral graph;Theoretical and Mathematical Physics;2022-11