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