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Determining the symmetries of difference equations

Xenitidis, Pavlos (2018) Determining the symmetries of difference equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2219). ISSN 1364-5021. E-ISSN 1471-2946. (doi:10.1098/rspa.2018.0340)

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http://dx.doi.org/10.1098/rspa.2018.0340

Abstract

We derive the determining equations for the Nth-order generalized symmetries of partial difference equations defined on d consecutive quadrilaterals on the lattice using the theory of integrability conditions. We provide their algebraic formulation and develop the necessary theoretical framework for their analysis along with a systematic method for solving functional equations of the form T ( f ) + Af + B=0. Our approach is algorithmic and can be easily implemented in symbolic computations. We demonstrate our approach by deriving the symmetries of various equations and discuss certain applications and extensions of the theory.

Item Type: Article
DOI/Identification number: 10.1098/rspa.2018.0340
Uncontrolled keywords: d-quad difference equations, symmetries, integrability conditions, determining equations
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Pavlos Xenitidis
Date Deposited: 29 Nov 2018 12:35 UTC
Last Modified: 09 Jul 2019 13:29 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70451 (The current URI for this page, for reference purposes)
Xenitidis, Pavlos: https://orcid.org/0000-0003-4091-7270
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