The non-isospectral modified Kadomtsev-Petviashvili equation with self-consistent sources and its coupled system

A new algebraic method called 'source generation procedure' is applied to construct non-isospectral soliton equations with self-consistent sources. As results, the non-isospectral modified Kadomtsev-Petviashvili equation with self-consistent sources (mKPESCS) and its Gramm-type determinant solutions are obtained by using the source generation procedure. Furthermore, a new coupled system of the non-isospectral mKPESCS and its Pfaffian solutions are constructed.