Results 21 to 30 of about 1,222,314 (174)
Unique positive solution for an alternative discrete Painlevé I equation [PDF]
, 2016 We show that the alternative discrete Painleve I equation has a unique solution which remains positive for all n >0. Furthermore, we identify this positive solution in terms of a special solution of the second Painleve equation involving the Airy ...
Clarkson, Peter +4 more
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The threefold way to quantum periods: WKB, TBA equations and q-Painlevé
SciPost Physics, 2023 We show that TBA equations defined by the BPS spectrum of $5d$ $\mathcal{N}=1$ $SU(2)$ Yang-Mills on $S^1\times \mathbb{R}^4$ encode the q-Painlevé III$_3$ equation.
Fabrizio Del Monte, Pietro Longhi
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Schlesinger transformations for Painlevé VI equation [PDF]
, 1995 A method to obtain the Schlesinger transformations for Painlevé VI equation is given. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated ...
Mugan, U. +3 more
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Ultradiscrete Painlevé VI with Parity Variables
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the
Kouichi Takemura, Terumitsu Tsutsui
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On the solvability of the discrete second Painlevé equation [PDF]
, 2011 The inverse monodromy method for studying the Riemann-Hilbert problem associated with classical Painlevé equations is applied to the discrete second Painlevé equation.
U Mugan +5 more
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Mathematics, 2023 The Chavy–Waddy–Kolokolnikov model for the description of bacterial colonies is considered. In order to establish if the mathematical model is integrable, the Painlevé test is conducted for the nonlinear ordinary differential equation which corresponds ...
Nikolay A. Kudryashov, Sofia F. Lavrova
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Lagrangians of Painlevé equations [PDF]
, 2020 In this article, we investigate Lagrangians of Painlevé equations. As is well known, Painlevé equations can be rewritten into Painlevé systems which are Hamiltonian systems.
Murata, Yoshihiro
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The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases [PDF]
, 2019 In this paper we consider the matrix nonautonomous semidiscrete (or lattice) equation D dtUn = (2n − 1)(Un+1 − Un−1)−1, as well as the scalar case thereof.
Gordoa, Pilar R. +4 more
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Discrete Dynamics in Nature and Society, 2012 The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property.
Yali Shen, Fengqin Zhang, Xiaomei Feng
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Painlevé test and the first Painlevé hierarchy [PDF]
, 1999 Starting from the first Painlevé equation, Painlevé type equations of higher order are obtained by using the singular point ...
Jrad F., Muǧan, U.
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