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.
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