Skip to main content

On the Lagrangian formulation of multidimensionally consistent systems

Xenitidis, Pavlos, Nijhoff, Frank W., Lobb, Sarah (2011) On the Lagrangian formulation of multidimensionally consistent systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2135). pp. 3295-3317. ISSN 1364-5021. (doi:10.1098/rspa.2011.0124) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:50067)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://doi.org/10.1098/rspa.2011.0124

Abstract

Multidimensional consistency has emerged as a key integrability property for partial difference equations (P?Es) defined on the ‘space–time’ lattice. It has led, among other major insights, to a classification of scalar affine-linear quadrilateral P?Es possessing this property, leading to the so-called Adler–Bobenko–Suris (ABS) list. Recently, a new variational principle has been proposed that describes the multidimensional consistency in terms of discrete Lagrangian multi-forms. This description is based on a fundamental and highly non-trivial property of Lagrangians for those integrable lattice equations, namely the fact that on the solutions of the corresponding P?E the Lagrange forms are closed, i.e. they obey a closure relation. Here, we extend those results to the continuous case: it is known that associated with the integrable P?Es there exist systems of partial differential equations (PDEs), in fact differential equations with regard to the parameters of the lattice as independent variables, which equally possess the property of multidimensional consistency. In this paper, we establish a universal Lagrange structure for affine-linear quad-lattices alongside a universal Lagrange multi-form structure for the corresponding continuous PDEs, and we show that the Lagrange forms possess the closure property.

Item Type: Article
DOI/Identification number: 10.1098/rspa.2011.0124
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: 07 Aug 2015 15:10 UTC
Last Modified: 29 May 2019 15:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/50067 (The current URI for this page, for reference purposes)
  • Depositors only (login required):