Connection formulae for Painlevé V functions. II: the \(\delta\) function Bose gas problem
type: Item
instance of: scholarly article
title: Connection formulae for Painlevé V functions. II: the \(\delta\) function Bose gas problem
zbMATH Open document ID: 0656.35114
DOI: 10.1016/0167-2789(86)90030-8
author: Barry M. McCoy
author: Shuang Tang
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: [For part I see ibid. 19, 42-72 (1986; Zbl 0639.58041).] We continue our study of those Painlevé V equations which admit a one- parameter family of solutions analytic at the origin and solve the global problem of connecting the 2-parameter expansion about \(t=0\) with the 2- parameter expansion valid for \(t\to \pm i\infty\). A special case of our results is applied to the study of the one-particle reduced density matrix of the one-dimensional gas of impenetrable bosons. We also use our results to obtain a 2-parameter connection formula for a class of Painlevé III functions.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4071522
zbMATH Keywords: Painlevé V equations
zbMATH Keywords: one-parameter family of solutions
zbMATH Keywords: 2-parameter expansion
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90030-8
OpenAlex ID: W2118231933
cites work: Connection formulae for Painlevé V functions
cites work: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
cites work: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
cites work: Monodromy problem and the boundary condition for some Painlevé equations
cites work: Q5824493
cites work: Q4112233
description: scientific article; zbMATH DE number 4071522