The gauge transformations of the constrained q-deformed KP hierarchy

In this paper, we mainly study the gauge transformations of the constrained q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy. Different from the usual case, we have to consider the additional constraints on the Lax operator of the constrained q-deformed KP hierarchy, since the form of the Lax operator must be kept when constructing the gauge transformations. For this reason, the selections of generating functions in elementary gauge transformation operators TD and TI must be very special, which are from the constraints in the Lax operator. At last, we consider the successive applications of n-step of TD and k-step of TI gauge transformations.