The non-isospectral and variable-coefficient KP equation with self-consistent sources and new coupled system

The non-isospectral variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained for the first time by using the source generation procedure. Moreover, a new coupled system of the non-isospectral variable-coefficient KP equation with self-consistent sources is constructed by applying the source generation procedure and the coupled non-isospectral variable-coefficient KP equation without sources. The novel coupled system with sources cannot only be reduced to the coupled non-isospectral variable-coefficient KP equation, but also reduced to the non-isospectral variable-coefficient KP equation with self-consistent sources.

Research highlights
► The non-isospectral variable-coefficient KP equation with self-consistent sources is constructed.
► A new coupled system with self-consistent sources is obtained.
► The source generation procedure is applied to the non-isospectral variable-coefficient KP equation.