Results 101 to 110 of about 1,141,931 (185)

Supersymmetric Quantum Mechanics and Painlevé IV Equation

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.
doaj   +1 more source

An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)

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
doaj   +1 more source

Isomonodromy and Painlevé Type Equations, Case Studies

There is an abundance of equations of Painlevé type besides the classical Painlevé equations. Classifications have been computed by the Japanese school. Here we consider Painlevé-type equations induced by isomonodromic families of linear ODE's having at ...
van der Put, Marius, Top, Jaap
core   +1 more source

Constructing solutions to the ultradiscrete Painlevé equations [PDF]

, 1997
We investigate the nature of particular solutions to the ultra-discrete Painlevé equations. We start by analysing the autonomous limit and show that the equations possess an explicit invariant which leads naturally to the ultra-discrete analog of ...
D Takahashi, B Grammaticos, A Ramani, Y Ohta, T Tokihiro   +4 more
core  

An Extended Complex Method to Solve the Predator–Prey Model

Axioms
Through transformation and utilizing a novel extended complex method combining with the Weierstrass factorization theorem, Wiman–Valiron theory and the Painlevé test, new non-constant meromorphic solutions were constructed for the predator–prey model ...
Hongqiang Tu, Guoqiang Dang
doaj   +1 more source

Painlevé differential equations in the complex plane

, 2002
This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed ...
Gromak, Valerii I, Shimomura, Shun, Laine, Ilpo   +2 more
core  

Geometric Identification of Discrete Painlevé Equations

This thesis determines the type of a particular discrete Painlevé equation using a geometric approach based on Sakai theory. Previous work on discrete Painlevé equations has connected the dynamics of these equations to actions of their symmetry groups on
Moore, Logan
core   +1 more source

On Geometric-Analytic Aspects of Solvable Nonlinear Ordinary Differential Equations and Some Applications

Mathematics
A geometric-analytic approach to studying invariants of solvable nonlinear ordinary differential equations is developed. In particular, there is described in detail a general scheme of constructing solvable nonlinear ordinary differential equations ...
Anatolij K. Prykarpatski, Victor A. Bovdi, Petro Y. Pukach, Yarema A. Prykarpatsky, Myroslava I. Vovk   +4 more
doaj   +1 more source

Bäcklund Transformation for Discrete Painlevé Equations

, 2007
In this thesis we studied an algorithmic method for investigating transformation properties of discrete Painlevé equations. This method yields explicit transformations which relates the solutions of a given discrete Painlevé equation with either the ...
Abu Mugheisib, Ashraf A.
core  

Elliptic Asymptotic Behaviours of Continuous and Discrete Painlevé Equations [PDF]

, 2018
This thesis investigates the asymptotic behaviours of both continuous and discrete Painlevé equations as their independent variables approach complex infinity.
Liu, Qing
core