Addition Formulae of Discrete KP, q-KP and Two-Component BKP Systems**Supported by the Zhejiang Provincial Natural Science Foundation under Grant No. LY15A010004, the National Natural Science Foundation of China under Grant Nos. 11201251, 11571192 and the Natural Science Foundation of Ningbo under Grant No. 2015A610157. Jingsong He is supported by the National Natural Science Foundation of China under Grant No. 11271210,

Abstract

In this paper, we construct 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.