The Finite Discrete KP Hierarchy and the Rational Functions

Abstract

ABSTRACT: The set of all rational functions with any fixed denominator that simultaneously nullify in the infinite point is parametrized by means of a well-known integrable system: a finite dimensional version of the discrete KP hierarchy. This type of study was originated in Y. Nakamura’s works who used others integrable systems. Our work proves that the finite discrete KP hierarchy completely parametrizes the space RatΛn of rational functions of the form fx qx/zn, where qx is a polynomial of order n − 1 with nonzero independent coefficent. More exactly, it is proved that there exists a bijection from RatΛn to the moduli space of solutions of the finite discrete KP hierarchy and a compatible linear system.