Open problems for Painlevé equations (Q2633019): Difference between revisions

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+Q3995225
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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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+Q5493481
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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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+Q3506778
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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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+Q5394330
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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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+Q5843703
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+Quasi-linear Stokes phenomenon for the second Painlev  transcendent
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+Q3999049
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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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+Q4395062
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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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+Q4830320
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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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+Q5296411
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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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+Q3579593
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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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+Q4389670
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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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