Abstract
The purpose of this article is to discuss an algebraic method for studying integrable differential-difference lattices with two discrete and one continuous independent variables. The main idea is based on the hypothesis that any integrable equation of this type admits an infinite sequence of reductions, which are Darboux integrable systems of differential-difference equations with two independent variables. To detect the Darboux integrability property of the reductions the authors use the characteristic Lie–Rinehart algebras. The hypothesis is confirmed by integrable three-dimensional lattices from the list given by Ferapontov et al (2015 Int. Math. Res. Not. 2015 4933). The required reductions are found for these lattices. Characteristic algebras corresponding to small-order reductions are described, integrals are calculated in both directions, which proves Darboux integrability. The approach might be useful for the integrable classification in 3D.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.