Reduction of lattice equations to the Painlevé equations: P${}_{\mathrm{IV}}$ and P${}_{\mathrm{V}}$

Abstract

In this paper, we construct a new relation between ABS equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

18 pages, 4 figures

References in corpus (4)

• Geometric Aspects of Painlevé Equations
• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case

Cited by in corpus (1)

• Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations