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Symmetries and conservation laws of the ABS equations and corresponding differential–difference equations of Volterra type

Xenitidis, Pavlos (2011) Symmetries and conservation laws of the ABS equations and corresponding differential–difference equations of Volterra type. Journal of Physics A: Mathematical and Theoretical, 44 (43). p. 435201. ISSN 1751-8113. (doi:10.1088/1751-8113/44/43/435201) (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)

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/10.1088/1751-8113/44/43/435201

Abstract

A sequence of canonical conservation laws for all the Adler–Bobenko–Suris (ABS) equations is derived and is employed in the construction of a hierarchy of master symmetries for equations H1–H3, Q1–Q3. For the discrete potential and Schwarzian KdV equations it is shown that their local generalized symmetries and nonlocal master symmetries in each lattice direction form centerless Virasoro-type algebras. In particular, for the discrete potential KdV, the structure of its symmetry algebra is explicitly given. Interpreting the hierarchies of symmetries of equations H1–H3, Q1–Q3 as differential–difference equations of Yamilov's discretization of Krichever–Novikov equation, corresponding hierarchies of master symmetries along with isospectral and nonisospectral zero curvature representations are derived for all of them.

Item Type: Article
DOI/Identification number: 10.1088/1751-8113/44/43/435201
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 15:08 UTC
Last Modified: 29 May 2019 15:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/50066 (The current URI for this page, for reference purposes)
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