Rational solutions to d-PIV
Jarmo Hietarinta, Kenji Kajiwara
TL;DR
This paper investigates the rational solutions of the discrete Painleve IV equation, deriving their structure and determinantal form, and exploring the effects of parameter shifts that disappear in the continuous limit.
Contribution
It introduces a new determinantal representation for rational solutions of d-PIV, highlighting a parameter shift that vanishes as the system approaches the continuous case.
Findings
Rational solutions generated via Schlesinger transformations.
Determinantal form of solutions including parameter shifts.
Parameter shift vanishes in the continuous limit.
Abstract
We study the rational solutions of the discrete version of Painleve's fourth equation d-PIV. The solutions are generated by applying Schlesinger transformations on the seed solutions -2z and -1/z. After studying the structure of these solutions we are able to write them in a determinantal form that includes an interesting parameter shift that vanishes in the continuous limit.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation