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

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

2001-02-02

arxiv.org/abs/nlin/0102003v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, LaTeX, no figures, to be published in Journal of Mathematical Physics

Scientific paper

10.1063/1.1357826

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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