CONSTRUCTING SOLUTIONS TO THE ULTRADISCRETE PAINLEVE EQUATIONS

We investigate the nature of particular solutions to the ultradiscrete Painleve equations. We start by analysing the autonomous limit and sh ow that the equations possess an explicit invariant which leads natura lly to the ultradiscrete analogue of elliptic functions. For the ultra discrete Painleve equations II and III we present special solutions re miniscent of the Casorati determinant ones which exist in the continuo us and discrete cases. Finally we analyse the discrete Painleve equati on I and show tow it contains both the continuous and the ultradiscret e ones as particular limits.