Berkeley, G and Igonin, S (2016) Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations. Journal of Physics A: Mathematical and Theoretical, 49 (27). 275201. ISSN 1751-8113
Abstract
Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux–Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita–Itoh–Bogoyavlensky, Toda, and Adler–Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and Theoretical. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Miura-type transformations, differential-difference equations, Lie group actions, Darboux-Lax representations, Narita-Itoh-Bogoyavlensky lattice, Toda lattice, Adler-Postnikov lattices |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 May 2016 09:35 |
Last Modified: | 01 Jul 2017 17:38 |
Published Version: | http://dx.doi.org/10.1088/1751-8113/49/27/275201 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8113/49/27/275201 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:99545 |