Some results on difference Painlevé IV equations

Jilong Zhang

doi:10.1080/10236198.2016.1255207

Some results on difference Painlevé IV equations

Jilong Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

University College London

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we investigate the family of difference Painlevé IV equation (w(z + 1) + w(z))(w(z) + w(z − 1)) = R(z,w) where R(z, w), where R(z,w), is rational in w and meromorphic in z. If equation assumes an admissible meromorphic solution of hyper-order ρ2(w) <1, we give the coefficients relations of all the classification, which are known as the difference Painlevé properties.

Original language	English
Pages (from-to)	1912-1929
Number of pages	18
Journal	Journal of Difference Equations and Applications
Volume	22
Issue number	12
DOIs	https://doi.org/10.1080/10236198.2016.1255207
State	Published - 1 Dec 2016

Keywords

Painlevé difference equation
iterate
meromorphic solution

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abstract = "In this paper, we investigate the family of difference Painlev{\'e} IV equation (w(z + 1) + w(z))(w(z) + w(z − 1)) = R(z,w) where R(z, w), where R(z,w), is rational in w and meromorphic in z. If equation assumes an admissible meromorphic solution of hyper-order ρ2(w) <1, we give the coefficients relations of all the classification, which are known as the difference Painlev{\'e} properties.",

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AB - In this paper, we investigate the family of difference Painlevé IV equation (w(z + 1) + w(z))(w(z) + w(z − 1)) = R(z,w) where R(z, w), where R(z,w), is rational in w and meromorphic in z. If equation assumes an admissible meromorphic solution of hyper-order ρ2(w) <1, we give the coefficients relations of all the classification, which are known as the difference Painlevé properties.

KW - Painlevé difference equation

KW - iterate

KW - meromorphic solution

UR - https://www.scopus.com/pages/publications/84996866018

U2 - 10.1080/10236198.2016.1255207

DO - 10.1080/10236198.2016.1255207

M3 - 文章

AN - SCOPUS:84996866018

SN - 1023-6198

VL - 22

SP - 1912

EP - 1929

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 12

ER -

Some results on difference Painlevé IV equations

Abstract

Keywords

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