Darboux transformations via Painlevé analysis

The interesting result obtained in this paper involves using the generalized singular manifold method to determine the Darboux transformations for the equations. It allows us to establish an iterative procedure to obtain multisolitonic solutions. This procedure is closely related to the Hirota -function method. In this paper, we report how to improve the singular manifold method when the equation has more than one Painlev? branch. The singular manifold method generalized in such a way is applied to a pair of equations in 2 + 1 dimensions

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