On the non-isospectral Kadomtsev–Petviashvili equation with self-consistent sources Original Research Article

A new procedure called ‘source generation’ is applied to construct non-isospectral soliton equations with self-consistent sources. As results, the non-isospectral Kadomtsev–Petviashvili equation with self-consistent sources (KPESCS) and its Gramm-type determinant solutions are obtained. Furthermore, the non-isospectral Pfaffianized-KP equation with self-consistent sources is constructed. This coupled system can not only be reduced to the non-isospectral Pfaffianized-KP equation, but also reduced to the non-isospectral KPESCS.