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Open problems for Painlevé equations (Q2633019)

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Language	Label	Description	Also known as
English	Open problems for Painlevé equations	scientific article

Statements

scholarly article

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Open problems for Painlevé equations (English)

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SIGMA. Symmetry, Integrability and Geometry: Methods and Applications

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publication date

8 May 2019

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full work available at URL

https://arxiv.org/abs/1901.10122

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zbMATH Keywords

Painlevé equations

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open problems

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Peter A. Clarkson

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MaRDI profile type

MaRDI publication profile

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A connection between nonlinear evolution equations and ordinary differential equations of P-type. I

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Numerical solution of the Cauchy problem for Painlevé III

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Numerical solution of the Cauchy problem for the Painlevé I and II equations

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Numerical solution of the Painlevé IV equation

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Numerical solution of the Painlevé V equation

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Numerical solution of the Painlevé VI equation

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A method for the numerical solution of the Painlevé equations

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A method for calculating the Painlevé transcendents

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Projective differential geometrical structure of the Painlevé equations

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Equivalence of ordinary differential equations \(y'' = R(x, y)y^{\prime 2} + 2Q(x, y)y' +P(x, y)\)

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Equivalence of Third‐Order Ordinary Differential Equations to Chazy Equations I–XIII

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Invariants of a family of scalar second-order ordinary differential equations

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Equivalence of second-order ordinary differential equations to Painlevé equations

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Invariants of a family of scalar second-order ordinary differential equations for Lie symmetries and first integrals

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Solution of the equivalence problem for the third Painlevé equation

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Application of uniform asymptotics to the second Painlevé transcendent

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Using invariants to solve the equivalence problem for ordinary differential equations.

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On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation

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Zeros of Large Degree Vorob’ev–Yablonski Polynomials via a Hankel Determinant Identity

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Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge

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On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review

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On the numerical evaluation of Fredholm determinants

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Transition asymptotics for the Painlevé II transcendent

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The nonlinear steepest descent approach to the singular asymptotics of the second Painlevé transcendent

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Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour

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Large-degree asymptotics of rational Painlevé-II functions: critical behaviour

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Differential equations with fixed critical points

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Equations différentielles du second ordre en Y et du second degré en Y dont l'intégrale générale est à points critiques fixes

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Transformees algébriques des équations du second ordre dont l'intégrale générale est à points critiques fixes

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Analytic results on the geometric entropy for free fields

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New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points

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Multi-critical unitary random matrix ensembles and the general Painlevé II equation

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On Airy Solutions of the Second Painlevé Equation

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New similarity reductions of the Boussinesq equation

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The second Painlev equation, its hierarchy and associated special polynomials

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A connection formula for the second Painlevé transcendent

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Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

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The Painlevé property. One century later

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All Binomial‐Type Painlevé Equations of the Second Order and Degree Three or Higher

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Painlevé Classification Problems Featuring Essential Singularities

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Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol <i>P</i>2

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Chazy Classes IX–XI Of Third‐Order Differential Equations

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Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol <i>P</i>1

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Chazy's second-degree Painlevé equations

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Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree

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Connection formulas for the Ablowitz–Segur solutions of the inhomogeneous Painlevé II equation

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On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation

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Large \(z\) asymptotics for special function solutions of Painlevé II in the complex plane

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Some open problems in random matrix theory and the theory of integrable systems

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Asymptotics for the painlevé II equation

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Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

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A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation

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On a unified approach to transformations and elementary solutions of Painlevé equations

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A numerical methodology for the Painlevé equations

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A computational exploration of the second Painlevé equation

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A computational overview of the solution space of the imaginary Painlevé II equation

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Painlevé II in random matrix theory and related fields

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Parametrization of solutions of the Lewis metric by a Painlevé transcendent III

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Painlevé differential equations in the complex plane

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A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation

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Is My ODE a Painlevé Equation in Disguise?

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UNITARY MATRIX MODELS AND PAINLEVÉ III

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Location of poles for the Hastings-McLeod solution to the second Painlevé equation

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Quasi-linear Stokes phenomenon for the second Painlev transcendent

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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II

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The Painlevé Connection Problem: An Asymptotic Approach. I

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Existence and uniqueness of tri-tronqu e solutions of the second Painlev hierarchy

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Geometric aspects of Painlevé equations

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The local equivalence problem for \(d^ 2y/dx^ 2=F(x,y,dy/dx)\) and the Painlevé transcendents

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Equivalence Classes of the Second Order Odes with the Constant Cartan Invariant

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Solution of the equivalence problem for the Painlevé IV equation

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Point classification of second order ODEs and its application to Painlevé equations

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``Painlevé 34'' equation: equivalence test

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation: I

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation: II

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Numerical approach to Painlevé transcendents on unbounded domains

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Normal form for second order differential equations

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The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability

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Lie point symmetries and ODEs passing the Painlevé test

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Unified approach to strings and vortices with soliton solutions

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The reduction problem and the inverse scattering method

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On the increasing tritronquée solutions of the Painlevé-II equation

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Point equivalence of second-order ODEs: maximal invariant classification order

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Padé approximations for Painlevé I and II transcendents

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Tronquée solutions of the Painlevé II equation

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Distributions of poles to Painlevé transcendents via Padé approximations

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A coalescent diagram of the Painlevé equations from the viewpoint of isomonodromic deformations

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Polynomial Hamiltonians associated with Painleve equations. I

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Polynomial Hamiltonians associated with Painleve equations. II: Differential equations satisfied by polynomial Hamiltonians

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Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)

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Numerical solution of Riemann-Hilbert problems: Painlevé II

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A general framework for solving Riemann-Hilbert problems numerically

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Numerical solution of Riemann-Hilbert problems: random matrix theory and orthogonal polynomials

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Nonlinear Steepest Descent and Numerical Solution of Riemann‐Hilbert Problems

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Integrable Hamiltonian systems and interactions through quadratic constraints

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Painlevé IV with both Parameters Zero: A Numerical Study

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Painlevé IV: A numerical study of the fundamental domain and beyond

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Rational surfaces associated with affine root systems and geometry of the Painlevé equations

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Second-order second degree Painlevé equations related with Painlevé I, II, III equations

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Second-order second-degree Painlevé equations related to Painlevé IV,V,VI equations

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent

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Random unitary matrices, permutations and Painlevé

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Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions

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The role of Painleve II in predicting new liquid crystal self-assembly mechanisms

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Solving local equivalence problems with the equivariant moving frame method

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Orthogonal Polynomials and Painlevé Equations

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Automatic deformation of Riemann-Hilbert problems with applications to the Painlevé II transcendents

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Pade Method to Painleve Equations

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Differential invariants of second order ODEs. I

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Identifiers

zbMATH Open document ID

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10.3842/SIGMA.2019.006

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2633019

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