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Painlevé Tests, Singularity Structure and Integrability (Q3613605)

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Language	Label	Description	Also known as
English	Painlevé Tests, Singularity Structure and Integrability	scientific article

Statements

scholarly article

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Painlevé Tests, Singularity Structure and Integrability (English)

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Andrew N. W. Hone

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publication date

12 March 2009

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full work available at URL

https://arxiv.org/abs/nlin/0502017

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zbMATH Keywords

Painlevé property

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integrability

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MaRDI profile type

MaRDI publication profile

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On the weak Kowalevski-Painlevé property for hyperelliptically separable systems

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Complex Angle Variables for Constrained Integrable Hamiltonian Systems

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The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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On the extension of the Painlevé property to difference equations

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Introduction to Classical Integrable Systems

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Model equations for long waves in nonlinear dispersive systems

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Integrable symplectic maps

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An integrable shallow water equation with peaked solitons

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Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes

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Hodograph Transformations of Linearizable Partial Differential Equations

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New similarity reductions of the Boussinesq equation

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On a shallow water wave equation

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

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Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations

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A perturbative Painlevé approach to nonlinear differential equations

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The two-singular manifold method: II. Classical Boussinesq system

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The Painlevé property. One century later

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

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Strings in less than one dimension and the generalized KdV hierarchies

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Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves

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Monodromy- and spectrum-preserving deformations. I

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Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation

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The Painlevé Property and Hirota's Method

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Factorization and Painleve analysis of a class of nonlinear third-order partial differential equations

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Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations

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Do integrable mappings have the Painlevé property?

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Shear-free relativistic fluids and the absence of movable branch points

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Diophantine integrability

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Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations

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Solutions of the first and second Painlevé equations are meromorphic

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Exact envelope-soliton solutions of a nonlinear wave equation

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

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Non-autonomous Hénon-Heiles systems

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Reciprocal transformations, Painlevé property and solutions of energy-dependent Schrödinger hierarchies.

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Prolongation algebras and Hamiltonian operators for peakon equations

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ELLIPTIC CURVES AND QUADRATIC RECURRENCE SEQUENCES

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An integrable hierarchy with a perturbed Hénon–Heiles system

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Singularity confinement for maps with the Laurent property

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DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS

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Painlevé transcendent describes quantum correlation function of the<b><i>XXZ</i></b>antiferromagnet away from the free-fermion point

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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

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A Direct Proof that Solutions of the Six Painlevé Equations Have No Movable Singularities Except Poles

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The radius of convergence and the well-posedness of the Painlevé expansions of the Korteweg - de Vries equation

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Painlevé classification of coupled Korteweg–de Vries systems

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Singularity confinement and algebraic integrability

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Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons

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Kowalevski top and genus-2 curves

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Perturbative symmetry approach

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Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations

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A unified approach to Painlevé expansions

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On a Schwarzian PDE associated with the KdV hierarchy

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The Weiss–Tabor–Carnevale Painlevé test and Burgers’ hierarchy

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The singular manifold method revisited

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Weak perturbative Painlevé analysis and descending series solutions

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A note on logarithms in the Painlevé test

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On the Identification of Integrable Equations Using Dirichlet Series

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Integrable mappings and soliton equations. II

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Bilinear discrete Painleve equations

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Arithmetical Method to Detect Integrability in Maps

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On Painlevé's equations I, II and IV

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The problem of integrable discretization: Hamiltonian approach

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Nonlinear ordinary differential equations resolvable with respect to an irregular singular point

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Integrable maps

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The Painlevé property for partial differential equations

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The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative

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On classes of integrable systems and the Painlevé property

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The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations

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Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations

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Identifiers

zbMATH Open document ID

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10.1007/978-3-540-88111-7_8

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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:3613605

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