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Asymptotic Solutions of the Discrete Painlevé Equation of Second Type
AbstractSeveral classes of asymptotic solutions of the discrete Painlevé equation of second type (dPII) for large values of the independent...
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Discrete Painlevé Equations: A Review
We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the...
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Special Solutions for Discrete Painlevé Equations
We construct special solutions for the discrete Painlevé equations. We start with a review of the corresponding solutions in the case of the...
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Painlevé Test and a Self-Similar Solution of the Kinetic Model
We study a one-dimensional system of equations for a discrete gas model (the McKean system). The McKean system is the Boltzmann kinetic equation of a...
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Dynamics of the Fifth Painlevé Foliation
The leaves of the Painlevé foliations appear as the isomonodromic deformations of a rank 2 linear connection on a moduli space of connections....
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q-Painlevé equations on cluster Poisson varieties via toric geometry
We provide a relation between the geometric framework for q -Painlevé equations and cluster Poisson varieties by using toric models of rational...
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Paul-Painlevé Analysis, Soliton and Periodic Wave in the Fractional Thermophoretic Motion Equation via Graphene Sheets
We focused on solitonic phenomena in substrate-supported graphene sheets by learning the solitons of fractional thermophoretic motion equation, which...
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The Defocusing Nonlinear Schrödinger Equation with a Nonzero Background: Painlevé Asymptotics in Two Transition Regions
In this paper, we address the Painlevé asymptotics of the solution in two transition regions for the defocusing nonlinear Schrödinger (NLS) equation...
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Universality for Multiplicative Statistics of Hermitian Random Matrices and the Integro-Differential Painlevé II Equation
We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. We consider one-cut regular polynomial...
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On Bäcklund transformations for some second-order nonlinear differential equations
AbstractWe obtain second-order nonlinear differential equations (and the associated Bäcklund transformations) with an arbitrary analytic function...
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Exactly Solvable Anharmonic Oscillator, Degenerate Orthogonal Polynomials and Painlevé II
Using WKB analysis, the paper addresses a conjecture of Shapiro and Tater on the similarity between two sets of points in the complex plane; on one...
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40 bilinear relations of q-Painlevé VI from \( \mathcal{N} \) = 4 super Chern-Simons theory
We investigate partition functions of the circular-quiver supersymmetric Chern-Simons theory which corresponds to the q -deformed Painlevé VI...
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Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method
The Painlevé-IV equation has two families of rational solutions generated, respectively, by the generalized Hermite polynomials and the generalized...
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Higher-order regulatable rogue wave and hybrid interaction patterns for a new discrete complex coupled mKdV equation associated with the fourth-order linear spectral problem
A new discrete complex coupled mKdV equation related to the fourth-order linear spectral problem is proposed. Firstly, we construct a new discrete...
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Canonical solution and singularity propagations of the nonlocal semi-discrete Schrödinger equation
In this paper, a nonlocal semi-discrete Schrödinger equation is first reduced from the combined Ragnisco–Tu equation with a nonlocal reduction, which...
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Painlevé Kernels and Surface Defects at Strong Coupling
It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg–Witten curves can be systematically studied via...
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Integrability – and How to Detect It
We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...