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YANG–BAXTER MAPS AND THE DISCRETE KP HIERARCHY

Published online by Cambridge University Press:  01 February 2009

S. KAKEI,
J. J. C. NIMMO and
R. WILLOX
S. KAKEI
Affiliation:
Department of Mathematics, Rikkyo University, Nishi-ikebukuro, Toshima-ku, Tokyo 171-8501, Japan e-mail: kakei@rkmath.rikkyo.ac.jp
J. J. C. NIMMO
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G128QQ, UK e-mail: jjcn@maths.gla.ac.uk
R. WILLOX
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan e-mail: willox@ms.u-tokyo.ac.jp
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Abstract

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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.

Keywords

39A1039A12

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009, pp. 107 - 119
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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