标题： KP-mKP层次的约化性质 显示英文标题

标题： Reduction properties of the KP-mKP hierarchy

摘要： 所谓的KP-mKP层次，这是通过带有两个导数的伪微分算子最近引入的，可以简化为Kadomtsev-Petviashvili（KP）、修正的KP（mKP）和两分量BKP层次。 在本文中，我们继续研究KP-mKP层次的约化性质，包括其$(n,m)$-约化及其约化到某个扩展的$r$-约化KP层次（$r$-阶Gelfand-Dickey及其波函数）。 作为副产品，我们证明了扩展的$r$-约化KP层次的Hirota方程来自于mKP层次的Hirota方程，这证实了Alexandrov在[J. High Energy Phys. 2015]中关于开放KdV层次的猜想。 显示英文摘要

摘要： 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 $(n,m)$-reduction and its reduction to a certain extended $r$-reduced KP hierarchy (the $r$-th Gelfand-Dickey together with its wave function). As a byproduct, we show that the Hirota equations of the extended $r$-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 ].