Yang-Baxter maps and the discrete KP hierarchy

Kakei, S., Nimmo, J.J.C. and Willox, R. (2009) Yang-Baxter maps and the discrete KP hierarchy. Glasgow Mathematical Journal, 51(A), pp. 107-119. (doi: 10.1017/S0017089508004825)

Abstract

We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with regard to the symmetry algebra underlying the reduced systems as well as the ultradiscretizability of these systems are discussed. A scheme for constructing ultradiscretizable reductions that give rise to Yang–Baxter maps is explained in two explicit examples.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Nimmo, Dr Jonathan
• Authors: Kakei, S., Nimmo, J.J.C., and Willox, R.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Journal Abbr.: Glas. Math. J.
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• ISSN (Online): 1469-509X
• Published Online: 17 February 2009
• Copyright Holders: Copyright © 2009 Cambridge University Press
• First Published: First published in Glasgow Mathematical Journal 51(A):107-119
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.