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arxiv: nlin/0102003 · v1 · submitted 2001-02-02 · 🌊 nlin.SI

Two binary Darboux transformations for the KdV hierarchy with self-consistent sources

Yunbo Zeng (1) , Wen-Xiu Ma (2) , Yijun Shao (1) ((1) Tsinghua University , China , (2) City University of Hong Kong , China) This is my paper
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keywords darbouxbinaryhierarchyself-consistentsourcestransformationstransformationauto-b
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Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides non auto-B\"{a}cklund transformation between two n-th KdV equations with self-consistent sources with different degrees. The formula for the m-times repeated binary Darboux transformations are presented. This enables us to construct the N-soliton solution for the KdV hierarchy with self-consistent sources.

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