YANG–BAXTER MAPS AND THE DISCRETE KP HIERARCHY
- 1 February 2009
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 51 (A) , 107-119
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.Keywords
This publication has 21 references indexed in Scilit:
- Yang–Baxter maps and integrable dynamicsPhysics Letters A, 2003
- Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang-Baxter EquationCommunications in Algebra, 2003
- On a Discrete Analogue of the Two-Dimensional Toda Lattice HierarchyPublications of the Research Institute for Mathematical Sciences, 2002
- Darboux transformations and the discrete KP equationJournal of Physics A: General Physics, 1997
- Box and ball system with a carrier and ultradiscrete modified KdV equationJournal of Physics A: General Physics, 1997
- From Soliton Equations to Integrable Cellular Automata through a Limiting ProcedurePhysical Review Letters, 1996
- Note on 'N-pseudoreductions' of the KP hierarchyJournal of Physics A: General Physics, 1987
- The direct linearizing transform for the τ function in three-dimensional lattice equationsPhysics Letters A, 1985
- Direct linearization of nonlinear difference-difference equationsPhysics Letters A, 1983
- On Hirota's difference equationsProceedings of the Japan Academy, Series A, Mathematical Sciences, 1982