The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

Abstract

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.

19 pages

References in corpus (2)

• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• Differential Fay identities and auxiliary linear problem of integrable hiearchies

Cited by in corpus (6)

• Differential equations for the KPZ and periodic KPZ fixed points
• Spin generalization of the Calogero-Moser hierarchy and the matrix KP hierarchy
• Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy
• Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero-Moser model
• Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy
• Multi-component Toda lattice hierarchy