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Moving frames: difference and differential-difference Lagrangians

White, Lewis C., Hydon, Peter E. (2024) Moving frames: difference and differential-difference Lagrangians. Symmetry, Integrability and Geometry: Methods and Applications, 20 . Article Number 006. ISSN 1815-0659. (KAR id:104622)


This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's Theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the Nonlinear Schroedinger Equation.

Item Type: Article
Additional information: For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Uncontrolled keywords: moving frames; difference equations; differential-difference equations; variational calculus; Noether's Theorem
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA387 Basic Lie theory
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Peter Hydon
Date Deposited: 15 Jan 2024 16:24 UTC
Last Modified: 08 Feb 2024 14:36 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

White, Lewis C..

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Hydon, Peter E..

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