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