Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions

Yang Shi; Nalini Joshi

doi:10.1098/rspa.2011.0167

Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions

Yang Shi, Nalini Joshi

Research output: Contribution to journal › Article

8 Citations (Scopus)

Abstract

In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)⁽¹⁾. We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlevé equations.

Original language	English
Pages (from-to)	3443-3468
Number of pages	26
Journal	PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume	467
Issue number	2136
DOIs	https://doi.org/10.1098/rspa.2011.0167
Publication status	Published - 8 Dec 2011
Externally published	Yes

Keywords

q-discrete
Painlevé equations
discrete equations
Iso-monodeomy deformation
Painlevé
Equations
Special solutions

Access to Document

10.1098/rspa.2011.0167Licence: In Copyright

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions'. Together they form a unique fingerprint.

Cite this

@article{b48067d89387437a8cee80d950e380d2,

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

abstract = "In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)(1). We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlev{\'e} equations.",

keywords = "q-discrete, Painlev{\'e} equations, discrete equations, Iso-monodeomy deformation, Painlev{\'e}, Equations, Special solutions",

author = "Yang Shi and Nalini Joshi",

year = "2011",

month = dec,

day = "8",

doi = "10.1098/rspa.2011.0167",

language = "English",

volume = "467",

pages = "3443--3468",

journal = "PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES",

issn = "1364-5021",

number = "2136",

}

TY - JOUR

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

T2 - I. Rational solutions

AU - Shi, Yang

AU - Joshi, Nalini

PY - 2011/12/8

Y1 - 2011/12/8

N2 - In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)(1). We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlevé equations.

AB - In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)(1). We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlevé equations.

KW - q-discrete

KW - Painlevé equations

KW - discrete equations

KW - Iso-monodeomy deformation

KW - Painlevé

KW - Equations

KW - Special solutions

UR - http://www.scopus.com/inward/record.url?scp=80755143284&partnerID=8YFLogxK

U2 - 10.1098/rspa.2011.0167

DO - 10.1098/rspa.2011.0167

M3 - Article

VL - 467

SP - 3443

EP - 3468

JO - PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

JF - PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

SN - 1364-5021

IS - 2136

ER -