SOLVING THE KP HIERARCHY BY GAUGE TRANSFORMATIONS

Abstract

We show that it is convenient to use "gauge" transformations (sometimes called explicit Backlund transformations) to generate new solutions for the KP hierarchy. Two particular kinds of gauge transformation operators, constructed out of the initial wave functions, are of fundamental importance in this approach. Through such gauge transformations, a very simple formula for the tau-function is obtained, encompassing and unifying all kinds of existing solutions. The corresponding free fermion representation and Baker functions for the new tau function can also be constructed.