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

TL;DR

This paper derives addition formulae for various integrable hierarchies like discrete KP, q-KP, and two-component BKP, demonstrating their equivalence to the hierarchies and highlighting the universality of addition formulae in integrable systems.

Contribution

It constructs and proves the addition formulae for multiple integrable hierarchies, establishing their equivalence and universality.

Findings

Addition formulae are equivalent to the hierarchies.

Addition formulae demonstrate universality in integrable systems.

The approach uses Hirota bilinear equations and τ functions.

Abstract

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 $\tau$ 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.