Discrete Dynamics in Nature and Society 
Volume 2008 (2008), Article ID 792632, 10 pages
doi:10.1155/2008/792632
Research Article

The Finite Discrete KP Hierarchy and the Rational Functions

Raúl Felipe1 and Nancy López2

 1CIMAT, 36000 Guanajuato, Mexico and ICIMAF , 10600 La Habana, Cuba
2Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Medellín 1226, Colombia
Received 27 November 2007; Accepted 6 June 2008

Recommended by Stevo Stević

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 RatΛ(n) of rational functions of the form f(x)=q(x)/zn, where q(x) is a polynomial of order n−1 with nonzero independent coefficent. More exactly, it is proved that there exists a bijection from RatΛ(n) to the moduli space of solutions of the finite discrete KP hierarchy and a compatible linear system.