From Discrete to Continuous Painlevé Equations: A Bilinear Approach

Abstract

We present the bilinear forms of the (continuous) Painlevé equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new and interesting result is the bilinearization of the P${}_{\mathrm{VI}}$ equation, something that was missing till now.

9 pages, plainTeX

References in corpus (1)

• Bilinear structure and Schlesinger transforms of the $q$-P${}_{\mathrm{III}}$ and $q$-P${}_{\mathrm{VI}}$ equations

Cited by in corpus (6)

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• Discrete gap probabilities and discrete Painleve equations
• Elliptic and Hyperelliptic Solutions of Discrete Painlevé I and Its Extensions to Higher Order Difference Equations
• Moduli spaces of d-connections and difference Painleve equations
• On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
• Recursion Relation of Hyperelliptic Psi-Functions of Genus Two