Geometric Baecklund-Darboux Transformations for the KP Hierarchy

摘要

In this paper it is shown that, if you have two planes in the Sato Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by Backlund-Darboux (shortly BD-)transformations. The pseudodifferential operator that performs this performs the transformation is shown to be built up in a geometric way from so-called elementary BD-transformations and is given here in a closed form. The corresponding action on the tau-function, associated to a plane in the Grassmannian, is also determined.