Darboux transformations from n-KdV to KP

The iterated Darboux transformations of an ordinary differential operator are constructively parametrized by an infinite-dimensional Grassmannian of finitely supported distributions. In the case that the operator depends on time parameters so that it is a solution to the n-KdV hierarchy, it is shown that the transformation produces a solution of the KP hierarchy. The standard definitions of the theory of tau-functions are applied to this Grassmannian and it is shown that these new tau-functions are quotients of KP tau-functions. The application of this procedure for the construction of 'higher rank' KP solutions is discussed.