MULTILINEAR FORMS ASSOCIATED WITH THE YAJIMA-OIKAWA SYSTEM

It is well known that the Kadomtsev-Petviashvili hierarchy (KP hierarc hy) is compatible with generalized k-constraints of the type (L(k))(-) = q partial derivative(-1)r. Those constraints are leading to integra ble 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 t au-function of the KP hierarchy has been studied: it adds trilinear eq uations to the set of bilinear ones. In this paper we shall derive a q uattro and a quintolinear equation for the tau-function of the KP hier archy under the 2-constraint.