Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 035, 16 pages      arXiv:1212.1952

On Addition Formulae of KP, mKP and BKP Hierarchies

Yoko Shigyo
Department of Mathematics, Tsuda College, Kodaira, Tokyo, 187-8577, Japan

Received December 12, 2012, in final form April 04, 2013; Published online April 23, 2013

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.

Key words: KP hierarchy; modified KP hierarchy; BKP hierarchy.

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