Binlinear identities and Hirota's bilinear forms for an extended Kadomtsev-Petviashvili hierarchy

Runliang LIN Tsinghua University, Beijing ,China Xiaojun LIU China Agricultural University, China Yunbo ZENG Tsinghua University, Beijing ,China

Mathematical Physics mathscidoc:1702.22012

Journal of Nonlinear Mathematical Physics, 20, 214, 2013
In this paper, we construct the bilinear identities for the wave functions of an extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchy with particular extended flows. By introducing an auxiliary parameter, whose flow corresponds to the so-called squared eigenfunction symmetry of KP hierarchy, we find the tau-function for this extended KP hierarchy. It is shown that the bilinear identities will generate all the Hirota's bilinear equations for the zero-curvature forms of the extended KP hierarchy, which includes two types of KP equation with self-consistent sources (KPSCS). It seems that the Hirota's bilinear equations obtained in this paper for KPSCS are in a simpler form by comparing with the results by X.B. Hu and H.Y. Wang.
KP hierarchy; bilinear identity; Hirota's bilinear form
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@inproceedings{runliang2013binlinear,
  title={Binlinear identities and Hirota's bilinear forms for an extended Kadomtsev-Petviashvili hierarchy},
  author={Runliang LIN, Xiaojun LIU, and Yunbo ZENG},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217163904974084451},
  booktitle={Journal of Nonlinear Mathematical Physics},
  volume={20},
  pages={214},
  year={2013},
}
Runliang LIN, Xiaojun LIU, and Yunbo ZENG. Binlinear identities and Hirota's bilinear forms for an extended Kadomtsev-Petviashvili hierarchy. 2013. Vol. 20. In Journal of Nonlinear Mathematical Physics. pp.214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217163904974084451.
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