Discrete Equations from BäckLund Transformations of the Fifth Painlevé Equation [PDF]
Math Phys Anal GeomIn this paper discrete equations are derived from Bäcklund transformations of the fifth Painlevé equation, including a new discrete equation which has ternary symmetry.
Clare Dunning +2 more
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Supersymmetric Quantum Mechanics and Painlevé IV Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation.
David Bermúdez, David J. Fernández C.
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A novel heuristic Morlet wavelet neural network design for the painlevé equation-II arising in nonlinear optics [PDF]
Scientific ReportsThe current investigations present the novel structure of Morlet wavelet neural network (MWNN) for the numerical solutions of Painlevé equation-II arising in nonlinear optics. An error based fitness function is constructed using the sense of differential
Sundas Faisal +4 more
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Soliton structures for the (3 + 1)-dimensional Painlevé integrable equation in fluid mediums [PDF]
Scientific ReportsThe (3 + 1)-dimensional Painlevé integrable equation are a class of nonlinear differential equations with special properties, which play an important role in nonlinear science and are of great significance in solving various practical problems, such as ...
Jian-Guo Liu
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Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type A_6^{(1)}
Symmetry, Integrability and Geometry: Methods and Applications, 2011 An ultradiscrete system corresponding to the q-Painlevé equation of type A_6^{(1)}, which is a q-difference analogue of the second Painlevé equation, is proposed. Exact solutions with two parameters are constructed for the ultradiscrete system.
Mikio Murata
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Dynamics of the Painlevé-Ince Equation [PDF]
, 2023 The Painlevé-Ince differential equation y+ 3 yy+ y= 0 has been studied from many points of view.
Llibre, Jaume
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation [PDF]
, 2013 We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations
Clarkson, Peter +3 more
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AGT correspondence, (q-)Painlevè equations and matrix models
Nuclear Physics B, 2022 Painlevè equation for conformal blocks is a combined corollary of integrability and Ward identities, which can be explicitly revealed in the matrix model realization of AGT relations.
A. Mironov +3 more
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The master Painlevé VI heat equation [PDF]
, 2014 4 pages, no figure. To appear, Comptes rendus, section mathe'matiques, bilingueGiven the second order scalar Lax pair of the sixth Painlevé equation, we build a generalized heat equation with rational coefficients which does not depend any more on the ...
Robert Conte +3 more
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