Giambelli type formulae in the BKP hierarchy

Addition formulae of discrete KP, q-KP and two-component BKP systems

In this paper, we constructed the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld-Sokolov hierarchies. With the help of the Hirota bilinear equations and $τ$ functions of different kinds of KP hierarchies, we prove that these addition formulae are equivalent to these hierarchies. These studies show that the addition formula in the research of the integrable systems has good universality.

On Addition Formulae of KP, mKP and BKP Hierarchies

In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies those results had previously been proved by Noumi, Takasaki and Takebe by way of wave functions. Here we give alternative and direct proofs for the case of the KP and mKP hierarchies. Our method can equally be applied to the BKP hierarchy.

BKP 层级的连通 Bosonic \(n\)-点函数公式

A Formula for Connected Bosonic \(n\)-Point Functions for the BKP Hierarchy

本文通过将 BKP 层级嵌入 KP 层级，提出了其 tau-函数的连通 Bosonic n-点函数公式，并证明了该公式与 Wang 和 Yang 给出的公式等价。