Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations

Abstract

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

17 pages

References in corpus (2)

• Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation
• On the three-dimensional consistency of Hirota's discrete Korteweg-de Vries Equation