ar X iv : s ol v - in t / 9 50 50 05 v 1 3 0 M ay 1 99 5 Approximate Lie Group Analysis of a Model Advection Equation on an Unstructured Grid

ar X iv : s ol v - in t / 9 70 50 02 v 1 1 M ay 1 99 7 Rational solutions to d - P IV

We study the rational solutions of the discrete version of Painlevé’s fourth equation (d-PIV). The solutions are generated by applying Schlesinger transformations on the seed solutions −2z and −1/z. After studying the structure of these solutions we are able to write them in a determinantal form that includes an interesting parameter shift that vanishes in the continuous limit.

ar X iv : s ol v - in t / 9 90 50 05 v 2 1 7 M ay 1 99 9 The KP Hierarchy in Miwa coordinates ∗

A systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay’s identities are obtained. It is shown that in terms of these variables the KP hierarchy gives rise to a Darboux system describing an infinite-dimensional conjugate net.

ar X iv : q - a lg / 9 70 50 27 v 1 2 8 M ay 1 99 7 Jordanian U h , s gl ( 2 ) and its coloured realization

A two-parametric non-standard (Jordanian) deformation of the Lie algebra gl(2) is constructed, and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang-Baxter equation. The corresponding coloured quantum group is presented explicitly.

ar X iv : s ol v - in t / 9 80 50 02 v 1 7 M ay 1 99 8 On the Miura and Bäcklund transformations associated with the supersymmetric Gelfand - Dickey bracket

The supersymmetric version of the Miura and Bäcklund transformations associated with the supersymmetric Gelfand-Dickey bracket are investigated from the point of view of the Kupershmidt-Wilson theorem.

ar X iv : h ep - t h / 95 05 05 9 v 1 1 0 M ay 1 99 5 orthochronous The Conformal Spin and Statistics Theorem