Hierarchies of nonlinear q-difference equations from series of Lax pairs

Mike Hay

Abstract

We present two hierarchies of nonlinear, integrable q-difference equations, one of which includes a q-difference form of each of the second and fifth Painleve equations, qPII and qPV, the other includes qPIII. All the equations have multiple free parameters. A method to calculate a 2 X 2 Lax pair for each equation in the hierarchy is also given.