Results 11 to 20 of about 1,141,931 (185)
Quantum Painlevé Equations: from Continuous to Discrete [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We examine quantum extensions of the continuous Painlevé equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlevé equations II, IV and V.
Alfred Ramani +2 more
doaj +4 more sources
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
doaj +1 more source
On the polynomial solution of the first Painlevé equation
International Journal of Applied Mathematical Research, 2017 The Painlevé equations and their solutions arises in pure, applied mathematics and theoretical physics. In this manuscript we apply the Optimal Homotopy Asymptotic Method (OHAM) for solving the first Painlevé equation. Our approximation technique is based on the use of polynomial solutions, which are shown to be accurate when compared to the computed
D. Sierra Porta, L. A. Núñez
openaire +1 more source
On Properties of meromorphic solutions of difference Painlevé I and II equation
Global Journal of Mathematical Analysis, 2017 In this paper, we investigate some properties of finite order transcendental meromorphic solutions of difference Painlev \(\)\acute{e}\) I and II equations, and obtain precise estimations of exponents of convergence of poles of difference \(\)\Delta w(z)=w(z+1)-w(z)\) and divided difference \(\)\frac{\Delta w(z)}{w(z)}\), and of fixed points of \(\)w(z+
Weimin Xue, Yanmei Teng
openaire +2 more sources
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
core +1 more source
Geometry of Painlevé equations
, 2023 International audienceThe goal of the course is to provide a description of the foliation associated to the Painlevé VI equation. Painlevé equations form 6 families of differential equations, the first 5 arising from degenerescence of the 6th one, with 4
Loray, Frank
core +2 more sources
Open Problems for Painlevé Equations [PDF]
, 2019 In this paper some open problems for Painlevé equations are discussed. In particular the following open problems are described: (i) the Painlevé equivalence problem; (ii) notation for solutions of the Painlevé equations; (iii) numerical solution of ...
Clarkson, Peter, Clarkson, P.A.
core +1 more source
Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities [PDF]
Opuscula Mathematica, 2022 We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface.
Shunya Adachi
doaj +1 more source
Painlevé equations—nonlinear special functions [PDF]
, 2003 The six Painlevé equations (PI–PVI) were first discovered about a hundred years ago by Painlevéand his colleagues in an investigation of nonlinear second-order ordinary differential equations.
Clarkson, Peter +2 more
core +1 more source
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations [PDF]
, 2013 We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations.
Clarkson, Peter
core +1 more source