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

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

2004-12-28

arxiv.org/abs/nlin/0412070v1

Journal of Physics A: Mathematical and General,37(2004) 7143-7162

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, no figures

Scientific paper

10.1088/0305-4470/37/28/006

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-B\"{a}cklund 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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