[BOOK][B] Orthogonal polynomials and Painlevé equations
W Van Assche - 2017 - books.google.com
There are a number of intriguing connections between Painlevé equations and orthogonal
polynomials, and this book is one of the first to provide an introduction to these. Researchers …
polynomials, and this book is one of the first to provide an introduction to these. Researchers …
Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method
RJ Buckingham, PD Miller - Constructive Approximation, 2022 - Springer
The Painlevé-IV equation has two families of rational solutions generated, respectively, by
the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply …
the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply …
Poles of Painlevé IV rationals and their distribution
D Masoero, P Roffelsen - SIGMA. Symmetry, Integrability and Geometry …, 2018 - emis.de
We study the distribution of singularities (poles and zeros) of rational solutions of the
Painlevé IV equation by means of the isomonodromic deformation method. Singularities are …
Painlevé IV equation by means of the isomonodromic deformation method. Singularities are …
Rational solutions of the Painlevé-III equation: large parameter asymptotics
The Painlevé-III equation with parameters Θ _0= n+ m Θ 0= n+ m and Θ _ ∞= m-n+ 1 Θ∞=
m-n+ 1 has a unique rational solution u (x)= u_n (x; m) u (x)= un (x; m) with u_n (∞; m)= 1 un …
m-n+ 1 has a unique rational solution u (x)= u_n (x; m) u (x)= un (x; m) with u_n (∞; m)= 1 un …
On the algebraic solutions of the Painlevé-III (D7) equation
RJ Buckingham, PD Miller - Physica D: Nonlinear Phenomena, 2022 - Elsevier
The D 7 degeneration of the Painlevé-III equation has solutions that are rational functions of
x 1/3 for certain parameter values. We apply the isomonodromy method to obtain a Riemann …
x 1/3 for certain parameter values. We apply the isomonodromy method to obtain a Riemann …
Large-degree asymptotics of rational Painlevé-IV functions associated to generalized Hermite polynomials
R Buckingham - International Mathematics Research Notices, 2020 - academic.oup.com
The Painlevé-IV equation has three families of rational solutions generated by the
generalized Hermite polynomials. Each family is indexed by two positive integers and …
generalized Hermite polynomials. Each family is indexed by two positive integers and …
Rational solutions of the Painlevé‐III equation
All of the six Painlevé equations except the first have families of rational solutions, which are
frequently important in applications. The third Painlevé equation in generic form depends on …
frequently important in applications. The third Painlevé equation in generic form depends on …
A -Steepest Descent Method for Oscillatory Riemann–Hilbert Problems
F Wang, WX Ma - Journal of Nonlinear Science, 2022 - Springer
We study the long-time asymptotic behavior of oscillatory Riemann–Hilbert problems (RHPs)
arising in the mKdV hierarchy (reducing from the AKNS hierarchy). Our analysis is based on …
arising in the mKdV hierarchy (reducing from the AKNS hierarchy). Our analysis is based on …
Rational solutions of Painlevé-II equation as Gram determinant
X Zhang, BY Lu - Chinese Physics B, 2023 - iopscience.iop.org
Abstract Under the Flaschka–Newell Lax pair, the Darboux transformation for the Painlevé-II
equation is constructed by the limiting technique. With the aid of the Darboux transformation …
equation is constructed by the limiting technique. With the aid of the Darboux transformation …
Rational solutions of Painlev\'{e}-II equation as Gram determinant
L Ling, BY Lu, X Zhang - arxiv preprint arxiv:2203.02647, 2022 - arxiv.org
Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II
equation is constructed by the limiting technique. With the aid of the Darboux transformation …
equation is constructed by the limiting technique. With the aid of the Darboux transformation …