Results 81 to 90 of about 1,141,931 (185)
Geometry behind one of the Painlevé III differential equations [PDF]
, 2018 The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics.
Hertling, Claus
core +1 more source
Variations for some Painlevé Equations [PDF]
, 2019 This paper first discusses irreducibility of a Painlevé equation P. We explain how the Painlevé property is helpful for the computation of special classical and algebraic solutions.
Top, Jakob; id_orcid +5 more
core +2 more sources
Spectral curves and discrete Painlevé equations [PDF]
, 2015 It is well known that isomonodromic deformations admit a Hamiltonian description. These Hamiltonians appear as coefficients of the characteristic equations of their Lax matrices, which define spectral curves for linear systems of differential and ...
Ormerod, Christopher M.
core
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
doaj +1 more source
Integrability of Discrete Equations Modulo a Prime
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We apply the ''almost good reduction'' (AGR) criterion, which has been introduced in our previous works, to several classes of discrete integrable equations.
Masataka Kanki
doaj +1 more source
Analytic solution of the Starobinsky model for inflation
European Physical Journal C: Particles and Fields, 2017 We prove that the field equations of the Starobinsky model for inflation in a Friedmann–Lemaître–Robertson–Walker metric constitute an integrable system. The analytical solution in terms of a Painlevé series for the Starobinsky model is presented for the
Andronikos Paliathanasis
doaj +1 more source
n-dimensional Bateman equation and Painlevé analysis of wave equations
, 2000 In the Painlevé analysis of nonintegrable partial differential equations one obtains differential constraints describing the movable singularity manifold.
Lindblom, Ove, Euler, Norbert
core +2 more sources
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.
core +1 more source
Rational Solutions of the Sasano System of Type A_5^{(2)}
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In this paper, we completely classify the rational solutions of the Sasano system of type A_5^{(2)}, which is given by the coupled Painlevé III system. This system of differential equations has the affine Weyl group symmetry of type A_5^{(2)}.
Kazuhide Matsuda
doaj +1 more source
Construction of a Lax Pair for the E_6^{(1)} q-Painlevé System
Symmetry, Integrability and Geometry: Methods and Applications, 2012 We construct a Lax pair for the $ E^{(1)}_6 $ $q$-Painlevé system from first principles by employing the general theory ofsemi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv ...
Christopher M. Ormerod +1 more
doaj +1 more source