q-Special Functions with |q|=1 and Their Applications to Discrete Integrable Systems

 

Author

Michitomo Nishizawa

Journal

J. Phys. A: Math. Gen. , 34 (2001), 10639-10647.

Abstract

Solutions for certain discrete integrable systems are constructed by using integral solutions for hypergeometric q-difference systems with |q| = 1. We apply a solution for Lauricella's D-type hypergeometric q-difference system with |q| = 1 to construct a solution for the discrete KP-hierarchy. Furthermore, an integral solution of a q-difference analogue of Bessel's equation is newly introduced and applied to construct a solution for a q-difference analogue of the cylindrical Toda equation with |q| = 1.

Cited by:

M. Nishizawa, Y. Ohta and S. Tsujimoto,
Some Aspects of Toda Molecule,
Preprint.

J.V. Stokman,
Askey-Wilson Functions and Quantum Groups,
mathCA/0301330,