A. Yu. Orlov, D. M. Scherbin
Published 2000-03-13, updated 2000-10-19Version 2
We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variable shifts parameters of hypergeometric functions. The role of additional symmetries in generating hypergeometric tau-functions is explained.
Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
