On Addition Formulae of KP, mKP and BKP Hierarchies

Abstract

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.

References in corpus (4)

• Integrable Hierarchies and Dispersionless Limit
• Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
• Differential Fay identities and auxiliary linear problem of integrable hiearchies
• Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit

Cited by in corpus (5)

• The master T-operator for the Gaudin model and the KP hierarchy
• Isotropic Grassmannians, Plücker and Cartan maps
• On the Expansion Coefficients of Tau-function of the BKP Hierarchy
• Tau functions, infinite Grassmannians and lattice recurrences
• Giambelli type formulae in the BKP hierarchy