English

Reduction properties of the KP-mKP hierarchy

Exactly Solvable and Integrable Systems 2025-01-10 v1

Abstract

The so-called KP-mKP hierarchy, which was introduced recently via pseudo-differential operators with two derivations, can be reduced to the Kadomtsev-Petviashvili (KP), the modified KP (mKP) and the two-component BKP hierarchies. In this note, we continue to study reductions properties of the KP-mKP hierarchy, including its (n,m)(n,m)-reduction and its reduction to a certain extended rr-reduced KP hierarchy (the rr-th Gelfand-Dickey together with its wave function). As a byproduct, we show that the Hirota equations of the extended rr-reduced KP hierarchy follow from those of the mKP hierarchy, which confirms a conjecture of Alexandrov on the open KdV hierarchy in [ J. High Energy Phys. 2015 ].

Keywords

Cite

@article{arxiv.2501.04984,
  title  = {Reduction properties of the KP-mKP hierarchy},
  author = {Lumin Geng and Jianxun Hu and Chao-Zhong Wu},
  journal= {arXiv preprint arXiv:2501.04984},
  year   = {2025}
}