Solving the constrained KP hierarchy by gauge transformations

Abstract

We solve the constrained Kadomtsev–Petviashvili (cKP) hierarchy by using the gauge transformation technique. We show that there are two kinds of gauge transformations which preserve the form of the Lax operator of the cKP hierarchy. One of them is differential type and the other is integral type. Through two such gauge transformations we obtain not only the Wronskian-type τ-functions for the cKP hierarchy, but also the binary-type τ-functions which have not been obtained before.