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The non-isospectral modified Kadomtsev-Petviashvili equation with self-consistent sources and its coupled system. (English) Zbl 1202.35261

Summary: 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 Gram-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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C05 Solutions to PDEs in closed form
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