A Lax pair for a lattice modified KdV equation, reductions to q-Painleve equations and associated Lax pairs

摘要

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