Singularity confinement in delay-differential Painlevé equations

Abstract

We study singularity confinement phenomena in examples of delay-differential Painlevé equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined. For three previously studied examples of delay-differential Painlevé equations, we describe all such singularities and show they are confined in the sense of our geometric description.

arXiv comment31 pages, 2 figures

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Cited by in corpus (3)

• A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations
• Integrable delay-difference and delay-differential analogues of the KdV, Boussinesq, and KP equations
• Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation