Singularity structure and algebraic properties of the differential-difference Kadomtsev–Petviashvili equation

We present a study of the differential-difference Kadomtsev–Petviashvili equation, which was derived using the differential-difference version of Satoʹs theory. We focus on the singularity structure of the equation, in particular the Painlevé property and singularity confinement. Moreover we study its symmetries (both Lie and generalized) and derive some interesting similarity reductions.