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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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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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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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Hybrid cubic and hyperbolic b-spline collocation methods for solving fractional Painlevé and Bagley-Torvik equations in the Conformable, Caputo and Caputo-Fabrizio fractional derivatives
In this paper, we approximate the solution of fractional Painlevé and Bagley-Torvik equations in the Conformable (Co), Caputo (C), and...
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Schlesinger Transformations for Algebraic Painlevé VI Solutions
Schlesinger ( S ) transformations can be combined with a direct rational ( R ) pull-back of a hypergeometric 2 × 2 system of ODEs to obtain
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Theory and Applications of the Elliptic Painlevé Equation
This note is intended to provide an introduction to the theory of discrete Painlevé equations focusing mainly on the elliptic difference case. The...
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Toda and Laguerre–Freud equations and tau functions for hypergeometric discrete multiple orthogonal polynomials
In this paper, the authors investigate the case of discrete multiple orthogonal polynomials with two weights on the step line, which satisfy Pearson...
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Padé Approximation for q-Painlevé/Garnier Equations
In this chapter, we consider the Padé approximation where the function \(\psi (x)\)...
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Precise Deviations for Discrete Ensembles
We consider precise deviations for discrete ensembles. For β = 2 case, we first establish an asymptotic formula of the Christoffel–Darboux kernel of...
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Special Function Solutions of Painlevé Equations: Theory, Asymptotics and Applications
In this paper we review the construction of special function solutions of the Painlevé differential equations. We motivate their study using the...
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Discrete Approximations and Optimality Conditions for Controlled Free-Time Swee** Processes
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the...
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Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions
A pair of one dimensional atomic chains which are coupled via the Klein-Gordon potential is considered in this study, with each chain experiencing...
