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pro vyhledávání: '"Pieter Roffelsen"'
Autor:
Pieter Roffelsen
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 099 (2012)
We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. It has been conjectured that the number of real roots of the nth Yablonskii-Vorob'ev
Externí odkaz:
https://doaj.org/article/4f622ffc13cf44dda8b59f06c797eefb
Autor:
Pieter Roffelsen
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 6, p 095 (2010)
We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained
Externí odkaz:
https://doaj.org/article/3aacb73f07e2423abb96516964a04607
Autor:
Nalini Joshi, Pieter Roffelsen
The Painlev\'e 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 that are explicitly solvable in terms of clas
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f5b495607f48611d235b52fd8843f2d
http://arxiv.org/abs/2212.11513
http://arxiv.org/abs/2212.11513
Autor:
Pieter Roffelsen, Nalini Joshi
Publikováno v:
Communications in Mathematical Physics. 384:549-585
A Riemann-Hilbert problem for a q-difference Painleve equation, known as $$q{\text {P}}_{{\text {IV}}}$$ , is shown to be solvable. This yields a bijective correspondence between the transcendental solutions of $$q{\text {P}}_{{\text {IV}}}$$ and cor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::66e54b95e68b11d8617f02c77ec6c394
https://doi.org/10.1007/s00220-021-04024-y
https://doi.org/10.1007/s00220-021-04024-y
Autor:
Pieter Roffelsen, Davide Masoero
We study the roots of the generalised Hermite polynomials $H_{m,n}$ when both $m$ and $n$ are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic region, and organise themselve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::31edfc00f8b8c1120011206a84660deb
Autor:
Pieter Roffelsen, Nalini Joshi
Publikováno v:
Nonlinearity. 29:3696-3742
For transcendental functions that solve non-linear $q$-difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin and infinity. We describe such solutions of a $q$-discrete Painlev\'e e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be5cd26462c474b3d826e49998be913d
https://doi.org/10.1088/0951-7715/29/12/3696
https://doi.org/10.1088/0951-7715/29/12/3696
Autor:
Pieter Roffelsen, Davide Masoero
We study the distribution of singularities (poles and zeros) of rational solutions of the Painlev\'e IV equation by means of the isomonodromic deformation method. Singularities are expressed in terms of the roots of generalised Hermite $H_{m,n}$ and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95895a43723aedc7b55a8041bda72a3d
http://arxiv.org/abs/1707.05222
http://arxiv.org/abs/1707.05222
Autor:
Nalini Joshi, Pieter Roffelsen
Publikováno v:
Nonlinearity; Dec2016, Vol. 29 Issue 12, p1-1, 1p