New type of a generalized variable-coefficient Kadomtsev-Petviashvili equation with self-consistent sources and its Grammian-type solutions

In this paper, the variable-coefficient Kadomtsev-Petviashvili (vcKP) equation with self-consistent sources is presented by two different methods, one is the source generation procedure, the other is the Pfaffianization procedure, and the solutions for the two new coupled systems are given through Grammian-type Pfaffian determinants.