A Lax pair for a lattice modified KdV equation, reductions toq-Painlevé equations and associated Lax pairs

We present a new, nonautonomous Lax pair for a lattice nonautomous modified Korteweg–deVries equation and show that it can be consistently extended multi-dimensionally, a property commonly referred to as being consistent around a cube. This nonautonomous equation is reduced to a series of q -discrete Painlevé equations, and Lax pairs for the reduced equations are found. A 2 × 2 Lax pair is given for a with multiple parameters and, also, for versions of and , all for the first time.