How to recover a subspace in an infinite-dimensional Grassmannian from its $\tau$-function or $\psi$-function?

Question

Solutions of the KP hierarchy are parametrized by an infinite-dimensional Grassmannian (Sato Grassmannian or Wilson's adelic Grassmannian). I heard somewhere that one can recover a subspace in the above infinite-dimensional Grassmannian by taking derivatives of its $\tau$-function or $\psi$-function (i.e. Baker-Akhiezer function). Is such a statement true and how to formulate it precisely/where to find it?