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 -reduction and its reduction to a certain extended -reduced KP hierarchy (the -th Gelfand-Dickey together with its wave function). As a byproduct, we show that the Hirota equations of the extended -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}
}