A Lax pair for a lattice modified KdV equation, reductions to q-Painlevé equations and associated Lax pairs
نویسندگان
چکیده
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 Painlevé equations, and Lax pairs for the reduced equations are found. A 2× 2 Lax pair is given for a qPIII with multiple parameters and, also, for versions of qPII and qPV, all for the first time. PACS number: 02.30.Ik
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