Mathematics

 In 1977, Hirota found the autonomous 2-dimensional difference-difference equation, which is a discrete analogue of the KdV equation. Then, in 1991 Capel, Nijhoff and Papageorgiou found its deautonomized version. The solutions of both versions have been investigated.
In this talk, we show that special solutions of its multiplicative (q-difference) version are given by
(1) solution to the q-Painleve equation of A5-type;
(2) Casorati determinants whose entries are given by basic hypergeometric functions.