Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: {II}. {H}ypergeometric solutions

Nalini Joshi; Yang Shi

doi:10.1098/rspa.2012.0224

Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: {II}. {H}ypergeometric solutions

Nalini Joshi
, Yang Shi

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

8 Citations (Scopus)

Abstract

This is the second part of our study of the solutions of a q -discrete second Painlevé equation (q-P_II)of type (A₂ + A₁)⁽¹⁾ via its iso-monodromy deformation problem. In part I, we showed how to use the q-discrete linear problem associated with q-P _II to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence of q-hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

Original language	English
Pages (from-to)	3247-3264
Number of pages	18
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	468
Issue number	2146
DOIs	https://doi.org/10.1098/rspa.2012.0224
Publication status	Published - 8 Oct 2012
Externally published	Yes

Keywords

discrete Painlevé equation
iso-mondromy deformation
special solutions
Discrete Painlevé equation
Iso-monodromy deformation
Special solutions

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10.1098/rspa.2012.0224Licence: In Copyright

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title = "Exact solutions of a q-discrete second Painlev{\'e} equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: \{II\}. \{H\}ypergeometric solutions",

abstract = "This is the second part of our study of the solutions of a q -discrete second Painlev{\'e} equation (q-PII)of type (A2 + A1)(1) via its iso-monodromy deformation problem. In part I, we showed how to use the q-discrete linear problem associated with q-P II to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence of q-hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.",

keywords = "discrete Painlev{\'e} equation, iso-mondromy deformation, special solutions, Discrete Painlev{\'e} equation, Iso-monodromy deformation, Special solutions",

author = "Nalini Joshi and Yang Shi",

year = "2012",

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day = "8",

doi = "10.1098/rspa.2012.0224",

language = "English",

volume = "468",

pages = "3247--3264",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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publisher = "Royal Society Publishing",

number = "2146",

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Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: {II}. {H}ypergeometric solutions. / Joshi, Nalini; Shi, Yang.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, No. 2146, 08.10.2012, p. 3247-3264.

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

TY - JOUR

T1 - Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions

T2 - {II}. {H}ypergeometric solutions

AU - Joshi, Nalini

AU - Shi, Yang

PY - 2012/10/8

Y1 - 2012/10/8

N2 - This is the second part of our study of the solutions of a q -discrete second Painlevé equation (q-PII)of type (A2 + A1)(1) via its iso-monodromy deformation problem. In part I, we showed how to use the q-discrete linear problem associated with q-P II to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence of q-hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

AB - This is the second part of our study of the solutions of a q -discrete second Painlevé equation (q-PII)of type (A2 + A1)(1) via its iso-monodromy deformation problem. In part I, we showed how to use the q-discrete linear problem associated with q-P II to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence of q-hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

KW - discrete Painlevé equation

KW - iso-mondromy deformation

KW - special solutions

KW - Discrete Painlevé equation

KW - Iso-monodromy deformation

KW - Special solutions

UR - http://purl.org/au-research/grants/ARC/DP0985615

UR - http://purl.org/au-research/grants/ARC/DP110102001

UR - https://www.scopus.com/pages/publications/84866378202

U2 - 10.1098/rspa.2012.0224

DO - 10.1098/rspa.2012.0224

M3 - Article

SN - 1364-5021

VL - 468

SP - 3247

EP - 3264

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2146

ER -

Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: {II}. {H}ypergeometric solutions

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Keywords

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