Results 1 to 10 of about 327 (99)
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations.
Eric M. Rains
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Vector perturbations of Kerr-AdS5 and the Painlevé VI transcendent
Journal of High Energy Physics, 2020 We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter μ introduced in [1] can be interpreted as apparent singularities of the resulting radial and angular ...
Julián Barragán Amado +2 more
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Cluster integrable systems, q-Painlevé equations and their quantization
Journal of High Energy Physics, 2018 We discuss the relation between the cluster integrable systems and q-difference Painlevé equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point.
M. Bershtein +2 more
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Wronskians, dualities and FZZT-Cardy branes
Nuclear Physics B, 2016 The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral ...
Chuan-Tsung Chan +3 more
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On the asymptotics of the real solutions to the general sixth Painlevé equation
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We study the general sixth Painlevé equation, develop, and justify the existence of several groups of asymptotics of its real solutions. Our methods also justify the differentiability of the asymptotics. Particular attention is paid to the solutions between 0 and 1.
Huizeng Qin, Youmin Lu
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Pure imaginary solutions of the second Painlevé equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 56, Page 2989-3009, 2004., 2004 We prove the existence and obtain local asymptotic formulas for pure imaginary solutions of the general second Painlevé equation.
Alisher S. Abdullayev
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On the asymptotic representation of the solutions to the fourth general Painlevé equation
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 13, Page 845-851, 2003., 2003 There have been many results on the asymptotics of the Painlevé transcendents in recent years, but the asymptotics of the fourth Painlevé transcendent has not been studied much. In this note, we study the general fourth Painlevé equation and develop an asymptotic representation of a group of its solutions as the independent variable approaches ...
Youmin Lu
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Symmetries in Connection Preserving Deformations
Symmetry, Integrability and Geometry: Methods and Applications, 2011 e wish to show that the root lattice of Bäcklund transformations of the q-analogue of the third and fourth Painlevé equations, which is of type (A_2+A_1)^{(1)}, may be expressed as a quotient of the lattice of connection preserving deformations ...
Christopher M. Ormerod
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The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We wish to explore a link between the Lax integrability of the q-Painlevé equations and the symmetries of the q-Painlevé equations. We shall demonstrate that the connection preserving deformations that give rise to the q-Painlevé equations may be thought
Christopher M. Ormerod
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A topological algorithm for the Fourier transform of Stokes data at infinity
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract We give a topological description of the behaviour of Stokes matrices under the Fourier transform from infinity to infinity in a large number of cases of one level. This explicit, algorithmic statement is obtained by building on a recent result of T.
Jean Douçot, Andreas Hohl
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