Painlev\'e IV and a third-order viewpoint
Classical Analysis and ODEs
2016-09-28 v1
Authors:
P. L. Robinson
Abstract
We take a third-order approach to the fourth Painlev\'e equation and indicate the value of such an approach to other second-order ODEs in the Painlev\'e-Gambier list of 50.
Cite
@article{arxiv.1609.08575,
title = {Painlev\'e IV and a third-order viewpoint},
author = {P. L. Robinson},
journal= {arXiv preprint arXiv:1609.08575},
year = {2016}
}
Related papers
View all related →
Algebraic Geometry · Mathematics
Symmetry in the Painlev\'e systems and their extensions to four-dimensional systems
Yusuke Sasano
2010-11-04
Classical Analysis and ODEs · Mathematics
4-Dimensional Power Geometry and its Application to $P_1$ -- $P_5$
Anastasia Parusnikova
2014-12-23
Classical Analysis and ODEs · Mathematics
Painlev\'e IV: roots and zeros
P. L. Robinson
2016-09-09
Exactly Solvable and Integrable Systems · Physics
Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlev\'{e} equation
Maria V. Demina, Nikolai A. Kudryashov
2007-05-23
Exactly Solvable and Integrable Systems · Physics
Painleve test and higher order differential equations
Ugurhan Mugan, Fahd Jrad
2009-09-29
Mathematical Physics · Physics
Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
David Bermudez, David J. Fernández C
2011-12-14
Exactly Solvable and Integrable Systems · Physics
Special polynomials associated with the fourth order analogue to the Painlev'e equations
Nikolai A. Kudryashov, Maria V. Demina
2015-06-26
Exactly Solvable and Integrable Systems · Physics
A study on the fourth q-Painlev\'e equation
Kenji Kajiwara, Masatoshi Noumi, Yasuhiko Yamada
2019-08-17
Classical Analysis and ODEs · Mathematics
The Painlev\'e transcendents with solvable monodromy
Kazuo Kaneko
2007-05-23
Algebraic Geometry · Mathematics
Order one equations with the Painlev\'e property
Georg Muntingh, Marius van der Put
2012-02-22
Exactly Solvable and Integrable Systems · Physics
A Lagrangian Description of the Higher-Order Painlev\'e Equations
A. Ghose Choudhury, Partha Guha, Nikolai A. Kudryashov
2015-06-03
Classical Analysis and ODEs · Mathematics
Rational solutions of the fourth and fifth Painlev\'{e} hierarchies
Anton Grigor'ev
2011-10-17
Exactly Solvable and Integrable Systems · Physics
Power solution expansions of the analogue tothe first Painleve equation
Aleksandr D. Bruno, Nikolai A. Kudryashov
2007-05-23
Differential Geometry · Mathematics
Metrisability of Painlev\'e equations
Felipe Contatto, Maciej Dunajski
2018-02-06
Classical Analysis and ODEs · Mathematics
Open Problems for Painlev\'e Equations
Peter A. Clarkson
2019-01-30
Exactly Solvable and Integrable Systems · Physics
Power expansions for solution of the fourth-order analog to the first Painlev\'{e} equation
Nikolai A. Kudryashov, Olga Yu. Efimova
2015-06-26
Classical Analysis and ODEs · Mathematics
Painleve Classification of Polynomial Ordinary Differential Equations of Arbitrary Order and Second Degree
Stanislav Sobolevsky
2014-10-13
Exactly Solvable and Integrable Systems · Physics
Linearisable systems and the Gambier approach
S. Lafortune, B. Grammaticos, A. Ramani
2007-05-23
Mathematical Physics · Physics
Higher order superintegrability, Painlev\'e transcendents and representations of polynomial algebras
Ian Marquette
2020-11-10
Mathematical Physics · Physics
Complex SUSY Transformations and the Painlev\'e IV Equation
David Bermúdez
2012-10-12
Classical Analysis and ODEs · Mathematics
Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms
Hina M. Dutt, Asghar Qadir
2016-11-25
Quantum Algebra · Mathematics
Quantum Painlev\'e Equations: from Continuous to Discrete
Hajime Nagoya, Basil Grammaticos, Alfred Ramani
2010-12-17
Exactly Solvable and Integrable Systems · Physics
Equivalence classes of the second order ODEs with the constant Cartan invariant
Vera V. Kartak
2015-05-28
Classical Analysis and ODEs · Mathematics
On matrix Painlev\'e-4 equations. Part 1: Painlev\'e--Kovalevskaya test
Irina Bobrova, Vladimir Sokolov
2022-12-06
Classical Analysis and ODEs · Mathematics
On Gevrey orders of power expansions of solutions to the third and fifth Painlev\'{e} equations
Anastasia Parusnikova
2013-10-22