Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations (Q879657)

scientific article; zbMATH DE number 5152622

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English	Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations	scientific article; zbMATH DE number 5152622

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instance of

scholarly article

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title

Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations (English)

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published in

Computational Methods and Function Theory

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publication date

14 May 2007

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zbMATH Keywords

hamiltonians

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rational solutions

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Painlevé equations

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Solitons and rational solutions of nonlinear evolution equations

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Q3925229

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Q5558293

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On a class of polynomials connected with the Korteweg-de Vries equation

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Recursion relations for unitary integrals, combinatorics and the Toeplitz lattice

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Nonlinear chains and Painlevé equations

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Proceedings of the seminar on classical and quantum integrable systems, Moscow, Russia, January 8--11, 2001

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Rational Solutions of Painlevé Equations

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Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem

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Algorithms for special integrals of ordinary differential equations

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Discriminants of Umemura polynomials associated to Painlevé III

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Q4222737

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Q4544988

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Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation

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Discrete gap probabilities and discrete Painlevé equations.

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Differential equations with fixed critical points. II

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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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Q3897296

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Q4893952

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Painlevé equations -- nonlinear special functions.

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The third Painlev equation and associated special polynomials

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The fourth Painlevé equation and associated special polynomials

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Remarks on the Yablonskii-Vorob'ev polynomials

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Special polynomials associated with rational solutions of the fifth Painlevé equation

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Q5710740

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Q5493481

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Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach

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The second Painlev equation, its hierarchy and associated special polynomials

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Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian

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

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Pole dynamics for elliptic solutions of the Korteweg-de Vries equation

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Q5641415

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Monodromy- and spectrum-preserving deformations. I

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

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From continuous to discrete Painlevé equations

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A method of linearization for Painlevé equations: Painlevé IV, V

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Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.

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Application of the τ‐function theory of Painlevé equations to random matrices: PV, PIII, the LUE, JUE, and CUE

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Discrete Painlev equations and random matrix averages

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Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations

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Lie symmetries of a generalised non-linear Schrodinger equation. III. Reductions to third-order ordinary differential equations

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The structure of the rational solutions to the Boussinesq equation

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Generating functions related to the Okamoto polynomials for the Painlevé IV equation

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Do integrable mappings have the Painlevé property?

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Q4061229

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Q3658306

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Q3791466

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Bäcklund transformations of the higher order Painlevé equations

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Q3147997

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Painlevé differential equations in the complex plane

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Q4889585

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Solutions of the first and second Painlevé equations are meromorphic

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Solutions of a modified third Painlevé equation are meromorphic

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Q4548124

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The meromorphic nature of the sixth Painlevé transcendents

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Crum transformation and rational solutions of the non-focusing nonlinear Schrödinger equation

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Q5843703

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Q4893948

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Generating function associated with the rational solutions of the Painlevé II equation

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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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Solitons and infinite dimensional Lie algebras

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Q5465716

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On a q-Difference Painlevé III Equation: II. Rational Solutions

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A generalization of determinant formulae for the solutions of Painlevé II and XXXIV equations

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On the Umemura polynomials for the Painlevé III equation

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Determinant structure of the rational solutions for the Painlevé II equation

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Determinant structure of the rational solutions for the Painlevé IV equation

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On poles of the rational solution of the Toda equation of Painlevé - II type

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On coefficients of Yablonskii-Vorob'ev polynomials

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Bispectral KP solutions and linearization of Calogero-Moser particle systems

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Q4793361

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Generalized Umemura polynomials.

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Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of \(n\) particles on a line

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Q5631445

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Q5644293

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Coulomb gas representation for rational solutions of the Painlevé equations

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Rational solutions of the \(A_4\) Painlevé equation

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On a Class of Algebraic Solutions to the Painlevé VI Equation, Its Determinant Formula and Coalescence Cascade

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On the rational solutions of q-Painlevé V equation

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Special Polynomials Associated with the Noumi-Yamada System of Type A5(1)

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A determinant formula for a class of rational solutions of Painlevé V equation

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Exact multi-soliton solution of the Benjamin-Ono equation

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Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation

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Q3729323

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Classical solutions of the third Painlevé equation

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A study of the alternate discrete Painlevé II equation

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Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique

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Q4830320

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Special polynomials associated with the Painlevé equations. II.

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Affine Weyl groups, discrete dynamical systems and Painlevé equations

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Umemura polynomials for the Painlevé V equation

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Symmetries in the fourth Painlevé equation and Okamoto polynomials

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On the \(\tau \)-function of the Painlevé equations

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

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Q3780146

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ALGEBRAIC RELATIONS AMONG SIX ADJACENT τ-FUNCTIONS RELATED TO THE FOURTH PAINLEVÉ SYSTEM

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Complex sine-Gordon-2: A new algorithm for multivortex solutions on the plane

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Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution

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Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions

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On a transcendental equation related to Painlevé III, and its discrete forms

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Discrete versions of the Painlevé equations

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On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy

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

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Two-dimensional lumps in nonlinear dispersive systems

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Backlund transformations of MKdV and Painleve equations

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Darboux transformations and the symmetric fourth Painlevé equation

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Value distribution of Painlevé transcendents of the first and the second kind

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Value distribution of Painlevé transcendents of the fifth kind

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The first, the second and the fourth Painlevé transcendents are of finite order.

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Growth of the first, the second and the fourth Painlevé transcendents

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Growth of modified Painlevé transcendents of the fifth and the third kind

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Calogero–Moser hierarchy and KP hierarchy

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On Painlevé's equations I, II and IV

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Value distribution of the Painlevé transcendents

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Boutroux's method vs. re-scaling. Lower estimates for the orders of growth of the second and fourth Painlevé transcendents

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Q4676347

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Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains

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Remarks on the Yablonskii-Vorob’ev polynomials

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Q4331083

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Representation of Umemura polynomials for the sixth Painlevé equation by the generalized Jacobi polynomials.

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Q4880419

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A system of particles equivalent to solitons

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Level-spacing distributions and the Airy kernel

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Fredholm determinants, differential equations and matrix models

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Q4435785

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Universal characters, integrable chains and the Painlevé equations

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Universal characters and \(q\)-Painlevé systems

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Tau functions of \(q\)-Painlevé III and IV equations

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Toda equation and special polynomials associated with the Garnier system

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\(q\)-Painlevé VI equation arising from \(q\)-UC hierarchy

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Folding transformations of the Painlevé equations

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On the transformation group of the second Painlevé equation

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Solutions of the second and fourth Painlevé equations, I

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Solutions of the third Painlevé equation I

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RATIONAL SOLUTIONS OF THE KADOMTSEV-PETVIASHVILI EQUATION AND HAMILTONIAN SYSTEMS

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On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy.

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Dressing chains and the spectral theory of the Schrödinger operator

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Painlevé equations from Darboux chains: I.PIII–PV

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Determinant formulas for the τ-functions of the Painlevé equations of type A

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Special polynomials and generalized Painlevé equations

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Identifiers

zbMATH Open document ID

1112.33015

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DOI

10.1007/BF03321618

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:879657