Discrete KP equation with self-consistent sources

• We rederive the discrete KP equation with sources (DKPS) using the squared eigenfunction symmetry method.
• We interpret the DKPS system in terms of the vectorial binary Darboux transformation of the Hirota bilinear KP equation.
• We show that the DKPS system is contained in the standard Hirota bilinear KP equation with sufficient number of variables.

We show that the discrete Kadomtsev–Petviashvili (KP) equation with sources obtained recently by the “source generalization” method can be incorporated into the squared eigenfunction symmetry extension procedure. Moreover, using the known correspondence between Darboux-type transformations and additional independent variables, we demonstrate that the equation with sources can be derived from Hirota's discrete KP equations but in a space of higher dimension. In this way we uncover the origin of the source terms as coming from multidimensional consistency of the Hirota system itself.