English

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

Exactly Solvable and Integrable Systems 2009-11-07 v1

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-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.

Keywords

Cite

@article{arxiv.nlin/0102003,
  title  = {Two binary Darboux transformations for the KdV hierarchy with self-consistent sources},
  author = {Yunbo Zeng and Wen-Xiu Ma and Yijun Shao},
  journal= {arXiv preprint arXiv:nlin/0102003},
  year   = {2009}
}

Comments

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