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

Yunbo Zeng·Wen-Xiu Ma·Yijun Shao
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Abstract

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-Bäcklund 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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Yunbo Zeng, Wen-Xiu Ma, Yijun Shao. 2001-02-02. Two binary Darboux transformations for the KdV hierarchy with self-consistent sources. https://doi.org/10.1063/1.1357826

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