Multilinear forms associated with the Yajima-Oikawa system

Abstract

It is well known that the Kadomtsev-Petviashvili hierarchy (KP hierarchy) is compatible with generalized k-constraints of the type ( L k ) − = q∂ −1 r. Those constraints are leading to integrable systems in 1 + 1 dimensions such as the AKNS system ( k = 1) or the Yajima-Oikawa system ( k = 2). The effect of the 1-constraint on the τ-function of the KP hierarchy has been studied: it adds trilinear equations to the set of bilinear ones. In this paper we shall derive a quattro and a quintolinear equation for the τ-function of the KP hierarchy under the 2-constraint.