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Hirota's discrete KdV equation is an integrable partial difference equationon $\mathbb{Z}^2$, which approaches the Korteweg-de Vries (KdV) equation in acontinuum limit. In this paper, we show that its multiplicative-discreteversions have the special solutions given by the solutions of $q$-Painlev\'eequations of types $A_J^{(1)}$ $(J=3,4,5,6)$.

Discrete Painlev\'e transcendent solutions to the multiplicative type discrete KdV equations