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Generalized Darboux transformations for the KP equation with self-consistent sources

Ting Xiao·Yunbo Zeng
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Abstract

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time $t$ for the KPESCS which, in contrast with the binary Darboux transformation of the KP equation, provides a non-auto-Bäcklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.

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Ting Xiao, Yunbo Zeng. 2004-12-28. Generalized Darboux transformations for the KP equation with self-consistent sources. https://doi.org/10.1088/0305-4470%2F37%2F28%2F006

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