NSTL国家科技图书文献中心

1. On the Crystal Limit of the q -Difference Sixth Painlevé Equation NSTL国家科技图书文献中心

Joshi, Nalini | Roffelsen, Pieter - 《Journal of nonlinear science》 - 2025,35(1) - 共30页

摘要：We consider the Riemann-Hilbert correspondence associated with the q-difference sixth Painlev & eacute; equation in the crystal limit, i.e., q -> 0documentclass[12pt]{minimal} usepackage{amsmath} usep...

关键词： Crystal limit | Painlev & eacute; equation . q -difference equation | Riemann-Hilbert correspondence | Segre surface

2. On q -Painlevé VI and the geometry of Segre surfaces NSTL国家科技图书文献中心

Roffelsen, Pieter - 《Nonlinearity》 - 2024,37(9) - ARTN 095024～ - 共116页

摘要：In the context of q-Painlev & eacute; VI with generic parameter values, the Riemann-Hilbert correspondence induces a one-to-one mapping between solutions of the nonlinear equation and points on an aff...

关键词： connection problems | Painlev & eacute; equations | Riemann-Hilbert problems | Segre surfaces | truncated asymptotics | DIFFERENCE | EQUATION | TRANSCENDENTS

3. On symmetric solutions of the fourth q-Painleve equation NSTL国家科技图书文献中心

Joshi, Nalini | Roffelsen, Pieter - 《Journal of physics, A. Mathematical and theoretical》 - 2023,56(18) - ARTN 185201～ - 共30页

摘要：The Painleve equations possess transcendental solutions y(t) with special initial values that are symmetric under rotation or reflection in the complex t-plane. They correspond to monodromy problems t...

关键词： symmetric solutions | monodromy problems | q-difference equations | Painleve equations

4. Roots of generalised Hermite polynomials when both parameters are large SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

Masoero, Davide | Roffelsen, Pieter - 《Nonlinearity》 - 2021,34(3) - 1663～1732 - 共70页

摘要：We study the roots of the generalised Hermite polynomials H-m,H-n when both m and n are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called...

关键词： generalised Hermite polynomials | Painleve IV | Boutroux curves | tritronquee solution | roots asymptotics

5. On the Riemann-Hilbert Problem for a q-Difference Painleve Equation NSTL国家科技图书文献中心

Joshi, Nalini | Roffelsen, Pieter - 《Communications in Mathematical Physics》 - 2021,384(1) - 549～585 - 共37页

摘要：A Riemann-Hilbert problem for a q-difference Painleve equation, known as qP(IV), is shown to be solvable. This yields a bijective correspondence between the transcendental solutions of qP(IV) and corr...

6. Poles of Painleve IV Rationals and their Distribution

Masoero, Davide | Roffelsen, Pieter - 《symmetry integrability and geometry-methods and applications》 - 2018,14 - 共49页

摘要：We study the distribution of singularities (poles and zeros) of rational solutions of the Painleve IV equation by means of the isomonodromic deformation method. Singularities are expressed in terms of...

关键词： Painleve fourth equation | singularities of Painleve transcendents | isomonodromic deformations | generalised Hermite polynomials | generalised Okamoto polynomials | LARGE-DEGREE ASYMPTOTICS | EQUATIONS | TRANSCENDENTS | DEFORMATION | TRITRONQUEE...

7. On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials

Roffelsen, Pieter - 《symmetry integrability and geometry-methods and applications》 - 2012,8 - 共9页

摘要：
We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painleve equation. It has...

关键词： second Painleve equation | rational solutions | real roots | interlacing of roots | Yablonskii-Vorob'ev polynomials | 2ND

8. Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them

Roffelsen, Pieter - 《symmetry integrability and geometry-methods and applications》 - 2010,6 - 共11页

摘要：
We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painleve equation. Divisibility properties ...

关键词： second Painleve equation | rational solutions | power series expansion | irrational roots | Yablonskii-Vorob'ev polynomials | PAINLEVE EQUATIONS | 2ND