Miura and auto-Bäcklund transformations for the discrete KP and mKP hierarchies and their constrained cases

In this paper, the Miura and auto-Bäcklund transformations for the dKP and mdKP hierarchies and their constrained cases are investigated. The combination of the Miura and reverse-Miura transformations are used to derive the auto-Bäcklund transformations. Also some applications of above results are considered.