Peter A. Clarkson

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All published works

Action	Title	Year	Authors
+	Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials	2023	Peter A. Clarkson Clare Dunning
+ PDF Chat	A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation	2023	Peter A. Clarkson Chun‐Kong Law Chia-Hua Lin
+	Generalized higher-order Freud weights	2023	Peter A. Clarkson Kerstin Jordaan Ana F. Loureiro
+ PDF Chat	Classical solutions of the degenerate fifth Painlevé equation	2023	Peter A. Clarkson
+	Classical Solutions of the Degenerate Fifth Painlevé Equation	2023	Peter A. Clarkson
+	Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials	2023	Peter A. Clarkson Clare Dunning
+	Generalised higher-order Freud weights	2022	Peter A. Clarkson Kerstin Jordaan Ana F. Loureiro
+ PDF Chat	A generalized sextic Freud weight	2021	Peter A. Clarkson Kerstin Jordaan
+	Generalised Airy polynomials	2021	Peter A. Clarkson Kerstin Jordaan
+	Cyclic Maya diagrams and rational solutions of higher order Painlevé systems	2020	Peter A. Clarkson David Gómez‐Ullate Yves Grandati Robert Milson
+ PDF Chat	Open Problems for Painlevé Equations	2019	Peter A. Clarkson
+	Open Problems for Painlevé Equations	2019	Peter A. Clarkson
+	Cyclic Maya diagrams and rational solutions of higher order Painlev\'e systems	2018	Peter A. Clarkson David Gómez‐Ullate Yves Grandati Robert Milson
+	On integrable Ermakov–Painlevé IV systems	2018	C. Rogers Andrew P. Bassom Peter A. Clarkson
+	Cyclic Maya diagrams and rational solutions of higher order Painlevé systems	2018	Peter A. Clarkson David Gómez‐Ullate Yves Grandati Robert Milson
+	Properties of generalized Freud polynomials	2017	Peter A. Clarkson Kerstin Jordaan
+ PDF Chat	Conservation Laws and Integral Relations for the Boussinesq Equation	2017	Adrian Ankiewicz Andrew P. Bassom Peter A. Clarkson Ellen Dowie
+ PDF Chat	Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System	2017	C. Rogers Peter A. Clarkson
+ PDF Chat	Rational solutions of the Boussinesq equation and applications to rogue waves	2017	Peter A. Clarkson Ellen Dowie
+	An algebraic proof for the Umemura polynomials for the third Painlevé equation	2016	Peter A. Clarkson Chun‐Kong Law Chia-Hua Lin
+	Symmetry Methods for Differential Equations	2016	Peter A. Clarkson
+ PDF Chat	On Airy Solutions of the Second Painlevé Equation	2016	Peter A. Clarkson
+ PDF Chat	Unique positive solution for an alternative discrete Painlevé I equation	2016	Peter A. Clarkson Ana F. Loureiro Walter Van Assche
+	A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation	2016	Peter A. Clarkson Chun‐Kong Law Chia-Hua Lin
+ PDF Chat	A Generalized Freud Weight	2015	Peter A. Clarkson Kerstin Jordaan Abey Sherif Kelil
+ PDF Chat	The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation	2013	Peter A. Clarkson Kerstin Jordaan
+ PDF Chat	Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations	2013	Peter A. Clarkson
+ PDF Chat	Vortices and Polynomials	2009	Peter A. Clarkson
+	Rational solutions of the classical Boussinesq system	2009	Peter A. Clarkson
+	Special Polynomials and Exact Solutions of the Dispersive Water Wave and Modified Boussinesq Equations	2009	Peter A. Clarkson Bryn W. M. Thomas
+	The fourth Painleve equation	2008	Peter A. Clarkson
+	The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials	2008	Galina Filipuk Peter A. Clarkson
+	Asymptotics of the second Painlevé equation	2008	Peter A. Clarkson
+	Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations	2006	Peter A. Clarkson
+	On the Lax Pairs of the Symmetric Painlevé Equations	2006	Ashoke Sen Andrew N. W. Hone Peter A. Clarkson
+ PDF Chat	Painlevé Analysis and Similarity Reductions for the Magma Equation	2006	Shirley E. Harris Peter A. Clarkson
+	SPECIAL POLYNOMIALS ASSOCIATED WITH RATIONAL AND ALGEBRAIC SOLUTIONS OF THE PAINLEV´ E EQUATIONS	2006	Peter A. Clarkson
+	THE LAX PAIR FOR THE MKDV HIERARCHY	2006	Peter A. Clarkson Nalini Joshi Marta Mazzocco
+	Darboux transformations and the symmetric fourth Painlevé equation	2005	Ashoke Sen Andrew N. W. Hone Peter A. Clarkson
+	Painlevé Equations and Associated Polynomials	2005	Peter A. Clarkson
+	SEMICLASSICAL SOLITON ENSEMBLES FOR THE FOCUSING NONLINEAR SCHRÖDINGER EQUATION (Annals of Mathematics Studies 154) By SPYRIDON KAMVISSIS, KENNETH D. T.-R. MCLAUGHLIN and PETER D. MILLER: 265 pp., £56.95, (US$84.50) £26.95 (US$39.95)(P), ISBN 0-691-11483-8/0-691-11482-X(P) (Princeton University Press, 2003)	2005	Peter A. Clarkson
+	Special polynomials associated with rational solutions of the fifth Painlevé equation	2004	Peter A. Clarkson
+	Remarks on the Yablonskii–Vorob'ev polynomials	2003	Peter A. Clarkson
+	The fourth Painlevé equation and associated special polynomials	2003	Peter A. Clarkson
+	PAINLEVÉ DIFFERENTIAL EQUATIONS IN THE COMPLEX PLANE (de Gruyter Studies in Mathematics 28) By VALERII I. GROMAK, ILPO LAINE and SHUN SHIMOMURA: 303 pp., US$89.95 (88.00 euro), ISBN 3-11-017379-4 (Walter de Gruyter, 2002)	2003	Peter A. Clarkson
+	The third Painlev equation and associated special polynomials	2003	Peter A. Clarkson
+	Painlevé equations—nonlinear special functions	2003	Peter A. Clarkson
+ PDF Chat	Hierarchies of Difference Equations and Bäcklund Transformations	2003	Peter A. Clarkson Andrew N. W. Hone Nalini Joshi
+	Symmetry, the Chazy equation and Chazy hierarchies	2002	Peter A. Clarkson Christopher M. Cosgrove
+ PDF Chat	Rational Solutions of an Extended Lotka-Volterra Equation	2002	Xiaofei Hu Peter A. Clarkson
+	On discrete Painlevé equations as Bäcklund transformations	2001	Peter A. Clarkson Edward R. Mansfield Helen Webster
+	The symmetry reductions of a turbulence model	2001	M. S. Bruzón Peter A. Clarkson M.L. Gandarias Елена Медина
+	Open problems in symmetry analysis	2001	Peter A. Clarkson Elizabeth L. Mansfield
+	Discrete equations and the singular manifold method	2000	P.G. Estévez Peter A. Clarkson
+	On the relation between the continuous and discrete Painlevé equations	2000	Peter A. Clarkson Elizabeth L. Mansfield Helen Webster
+	Similarity Reductions and Exact Solutions for the Two‐Dimensional Incompressible Navier–Stokes Equations	1999	D. Ludlow Peter A. Clarkson Andrew P. Bassom
+	Generalized Bäcklund transformation and new explicit solutions of the two-dimensional Toda equation	1999	Xing‐Biao Hu Peter A. Clarkson
+	Discrete equations and the singular manifold method	1999	P.G. Estévez Peter A. Clarkson
+	Symmetry Reduction and Exact Solutions of Nonlinear Partial Differential Equations	1999	Peter A. Clarkson P. Winternitz
+ PDF Chat	Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach	1999	Peter A. Clarkson Nalini Joshi Andrew Pickering
+ PDF Chat	Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations	1999	Peter A. Clarkson Thomas J. Priestley
+ PDF Chat	Symmetries and Integrability of Difference Equations: q -Special Functions and q -Difference Equations	1999	Peter A. Clarkson Frank Nijhoff
+	Shallow Water Wave Systems	1998	Peter A. Clarkson Thomas J. Priestley
+	Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations	1998	D. Ludlow Peter A. Clarkson Andrew P. Bassom
+ PDF Chat	Application of Uniform Asymptotics to the Second Painlevé Transcendent	1998	Andrew P. Bassom Peter A. Clarkson Chun‐Kong Law J. B. McLeod
+	Bäcklund transformations and nonlinear superposition formulae of a differential-difference KdV equation	1998	Xing-Bao Hu Peter A. Clarkson
+	Multicomponent equations associated to non-isospectral scattering problems	1997	Peter A. Clarkson Pilar R. Gordoa Andrew Pickering
+	Applications of the Differential Algebra Packagediffgrob2to Classical Symmetries of Differential Equations	1997	Elizabeth L. Mansfield Peter A. Clarkson
+	Symmetries of a class of nonlinear third-order partial differential equations	1997	Peter A. Clarkson Elizabeth L. Mansfield Thomas J. Priestley
+	Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation	1997	Elizabeth L. Mansfield Peter A. Clarkson
+ PDF Chat	The classical, direct, and nonclassical methods for symmetry reductions of nonlinear partial differential equations	1997	Peter A. Clarkson D. Ludlow Thomas J. Priestley
+	Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation and their application to discrete equations	1996	Peter A. Clarkson Andrew P. Bassom
+ PDF Chat	Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system	1996	Peter A. Clarkson Elizabeth L. Mansfield Alice E. Milne
+	Symmetry and the Chazy Equation	1996	Peter A. Clarkson Peter J. Olver
+ PDF Chat	On the application of solutions of the fourth Painlevé equation to various physically motivated nonlinear partial differential equations	1996	Andrew P. Bassom Peter A. Clarkson A. C. Hicks
+	Application of Uniform Asymptotics to the Second Painlev{é} Transcendent	1996	Andrew P. Bassom Peter A. Clarkson Chun‐Kong Law John Mcleod
+	Symmetries of a class of Nonlinear Third Order Partial Differential Equations	1996	Peter A. Clarkson Elizabeth L. Mansfield Thomas J. Priestley
+	Nonclassical symmetry reductions of the Boussinesq equation	1995	Peter A. Clarkson
+	Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation	1995	Andrew P. Bassom Peter A. Clarkson Andrew C. Hicks
+	Symmetry reductions and exact solutions of shallow water wave equations	1995	Peter A. Clarkson Elizabeth L. Mansfield
+	Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations	1995	Peter A. Clarkson Elizabeth L. Mansfield
+ PDF Chat	Algorithms for the Nonclassical Method of Symmetry Reductions	1994	Peter A. Clarkson Elizabeth L. Mansfield
+ PDF Chat	New exact solutions of the discrete fourth Painleve´equation	1994	Andrew P. Bassom Peter A. Clarkson
+	Symmetry Reductions, Exact Solutions, and Painlevé Analysis for a Generalized Boussinesq Equation	1994	Peter A. Clarkson D. Ludlow
+ PDF Chat	On a shallow water wave equation	1994	Peter A. Clarkson Elizabeth L. Mansfield
+ PDF Chat	New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations	1994	Peter A. Clarkson Simon Hood
+ PDF Chat	Symmetry reductions and exact solutions of a class of nonlinear heat equations	1994	Peter A. Clarkson Elizabeth L. Mansfield
+	Algorithms for the Nonclassical Method of Symmetry Reductions	1994	Peter A. Clarkson Elizabeth L. Mansfield
+	Symmetries and Exact Solutions of a 2+1-dimensional Sine-Gordon System	1994	Peter A. Clarkson Elizabeth L. Mansfield Alice E. Milne
+	Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations	1994	Peter A. Clarkson Elizabeth L. Mansfield
+	Backlund Transformations and Hierarchies of Exact Solutions for the Fourth Painleve Equation and their Application to Discrete Equations	1994	Peter A. Clarkson Andrew P. Bassom
+	Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation	1993	D. Ludlow Peter A. Clarkson
+	Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat Equations	1993	Peter A. Clarkson Elizabeth L. Mansfield
+	Rational Solutions and Bäcklund Transformations for the Third Painlevé Equation	1993	Alice E. Milne Peter A. Clarkson
+	Symmetry Reductions and Exact Solutions of the Davey-Stewartson System	1993	Simon Hood Peter A. Clarkson
+	Symmetries of the Nonlinear Heat Equation	1993	Peter A. Clarkson Elizabeth L. Mansfield
+	The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh-Nagumo equation	1992	M. C. Nucci Peter A. Clarkson
+	Dimensional reductions and exact solutions of a generalized nonlinear Schrodinger equation	1992	Peter A. Clarkson
+	The Painlevé‐Kowalevski and Poly‐Painlevé Tests for Integrability	1992	Martin D. Kruskal Peter A. Clarkson
+	Integral Equations and Connection Formulae for the Painlevé Equations	1992	Peter A. Clarkson J. B. McLeod
+	Inverse Scattering for Integro-Differential Equations	1991	M. A. Ablowitz Peter A. Clarkson
+	Remarks on Riemann-Hilbert problems	1991	M. A. Ablowitz Peter A. Clarkson
+	New exact solutions of the Boussinesq equation	1990	Peter A. Clarkson
+	Reductions of self-dual Yang-Mills fields and classical systems	1990	Sarbarish Chakravarty Mark J. Ablowitz Peter A. Clarkson
+	Painlevé Analysis and the Complete Integrability of a Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation	1990	Peter A. Clarkson
+	Examples of Nonclassical Similarity Reductions	1990	Peter A. Clarkson
+	New Similarity Reductions of Boussinesq-Type Equations	1990	Peter A. Clarkson
+	New similarity reductions and Painleve analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations	1989	Peter A. Clarkson
+	Hodograph Transformations of Linearizable Partial Differential Equations	1989	Peter A. Clarkson A. S. Fokas Mark J. Ablowitz
+	New similarity solutions for the modified Boussinesq equation	1989	Peter A. Clarkson
+	A connection formula for the second Painlevé transcendent	1988	Peter A. Clarkson J. B. McLeod
+	Painlevé analysis of the damped, driven nonlinear Schrödinger equation	1988	Peter A. Clarkson
+	The Painlevé tests and complete integrability	1987	Peter A. Clarkson
+	Painleve analysis of the non-linear Schrodinger family of equations	1987	Peter A. Clarkson C M Cosgrove
+ PDF Chat	Integrability of Klein–Gordon Equations	1986	Peter A. Clarkson John Mcleod Peter J. Olver A. Ramani
+	The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation	1986	Peter A. Clarkson
+	The Painlevé conjecture, the Painlevé property for partial differential equations and complete integrability	1986	Peter A. Clarkson
+	Remarks on the two-dimensional sine-Gordon equation and the Painlev� tests	1985	Peter A. Clarkson
+	The Painlevé property and a partial differential equation with an essential singularity	1985	Peter A. Clarkson
+	A note on solutions of Painlevé II	1982	Peter A. Clarkson John Mcleod
+	A connection formula for the Second Painlevé Transcendent	1982	Peter A. Clarkson J. B. McLeod

Common Coauthors

Coauthor	Papers Together
Elizabeth L. Mansfield	17
Andrew P. Bassom	11
Kerstin Jordaan	7
D. Ludlow	5
Chun‐Kong Law	5
Thomas J. Priestley	5
J. B. McLeod	4
Alice E. Milne	3
Andrew N. W. Hone	3
David Gómez‐Ullate	3
John Mcleod	3
Nalini Joshi	3
Ana F. Loureiro	3
Yves Grandati	3
Chia-Hua Lin	3
Robert Milson	3
Andrew Pickering	2
Ashoke Sen	2
Helen Webster	2
Mark J. Ablowitz	2
Simon Hood	2
A. C. Hicks	2
Ellen Dowie	2
P.G. Estévez	2
Clare Dunning	2
Peter J. Olver	2
C. Rogers	2
M. A. Ablowitz	2
Galina Filipuk	1
C M Cosgrove	1
Елена Медина	1
A. S. Fokas	1
Marta Mazzocco	1
Adrian Ankiewicz	1
Walter Van Assche	1
A. Ramani	1
Christopher M. Cosgrove	1
M. S. Bruzón	1
Frank Nijhoff	1
M. C. Nucci	1
Bryn W. M. Thomas	1
Abey Sherif Kelil	1
Xing-Bao Hu	1
Edward R. Mansfield	1
Sarbarish Chakravarty	1
Pilar R. Gordoa	1
Shirley E. Harris	1
M. L. Gandarias	1
Martin D. Kruskal	1
Xing‐Biao Hu	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Studies on the Painlev� equations	1986	Kazuo Okamoto	37
+	Ordinary Differential Equations	1945	A. T. Lonseth E. L. Ince	35
+	The Painlevé property for partial differential equations	1983	John Weiss M. Tabor G. F. Carnevale	30
+	A connection between nonlinear evolution equations and ordinary differential equations of P-type. I	1980	Mark J. Ablowitz A. Ramani Harvey Segur	29
+	On a unified approach to transformations and elementary solutions of Painlevé equations	1982	A. S. Fokas Mark J. Ablowitz	29
+	Nonlinear evolution equations and ordinary differential equations of painlevè type	1978	Mark J. Ablowitz A. Ramani Harvey Segur	24
+	A boundary value problem associated with the second painlev� transcendent and the Korteweg-de Vries equation	1980	S. P. Hastings John Mcleod	23
+ PDF Chat	Application of the τ-Function Theory¶of Painlevé Equations to Random Matrices:¶PIV, PII and the GUE	2001	Peter J. Forrester N. S. Witte	23
+ PDF Chat	Studies on the Painlevé equations	1986	Kazuo Okamoto	21
+ PDF Chat	Applications of lie groups to differential equations	1990	Peter J. Olver	21
+ PDF Chat	Monodromy- and spectrum-preserving deformations I	1980	H. Flaschka Alan C. Newell	21
+ PDF Chat	The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type	1983	John Mcleod Peter J. Olver	20
+	Exact Linearization of a Painlevé Transcendent	1977	Mark J. Ablowitz Harvey Segur	20
+	Symmetries and Differential Equations	1989	George W. Bluman Sukeyuki Kumei	20
+	Painlevé Differential Equations in the Complex Plane	2002	Valerii I. Gromak Ilpo Laine Shun Shimomura	19
+	Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II	1981	Michio Jimbo Tetsuji Miwa	18
+	Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation	1995	Andrew P. Bassom Peter A. Clarkson Andrew C. Hicks	17
+	New exact solutions of the Boussinesq equation	1990	Peter A. Clarkson	17
+	The computer calculation of Lie point symmetries of large systems of differential equations	1991	Bernard Champagne Willy Hereman P. Winternitz	17
+ PDF Chat	Determinant structure of the rational solutions for the Painlevé IV equation	1998	Kenji Kajiwara Yasuhiro Ohta	16
+ PDF Chat	Determinant structure of the rational solutions for the Painlevé II equation	1996	Kenji Kajiwara Yasuhiro Ohta	16
+ PDF Chat	Discrete Painlevé equations and their appearance in quantum gravity	1991	A. S. Fokas A. R. Its A. V. Kitaev	15
+	Inverse scattering and the boussinesq equation	1982	Percy Deift Carlos Tomei Eugene Trubowitz	15
+	A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs	1990	G. J. Reid	15
+	Linearization of the Boussinesq equation and the modified Boussinesq equation	1982	G. Quispel Frank Nijhoff H.W. Capel	15
+	The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative	1983	John Weiss	15
+	The construction of special solutions to partial differential equations	1986	Peter J. Olver Philip Rosenau	15
+	Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution	1991	Gregory J. Reid	14
+ PDF Chat	On the Umemura polynomials for the Painlevé III equation	1999	Kenji Kajiwara Tetsu Masuda	14
+	Similarity Methods for Differential Equations	1974	George W. Bluman Julian D. Cole	14
+	Symmetries of Differential Equations: From Sophus Lie to Computer Algebra	1988	Fritz Schwarz	13
+	From Gauss to Painlevé	1991	Katsunori Iwasaki Hironobu Kimura Shun Shimomura Masaaki Yoshida	13
+ PDF Chat	Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes	1911	Jean Chazy	13
+ PDF Chat	Classical solutions of the third Painlevé equation	1995	Yoshihiro Murata	13
+ PDF Chat	Applications of Lie Groups to Differential Equations	1993	Peter J. Olver	13
+	The fourth Painlevé equation and associated special polynomials	2003	Peter A. Clarkson	12
+	Lax pairs, Backlund transformations and special solutions for ordinary differential equations	1988	John Gibbon Alan C. Newell M. Tabor Y B Zeng	12
+	Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials	1995	Alphonse Magnus	12
+ PDF Chat	A generalization of determinant formulae for the solutions of Painlevé II and XXXIV equations	1999	Kenji Kajiwara Tetsu Masuda	12
+	From Continuous to Discrete Painlevé Equations	1993	A. S. Fokas B. Grammaticos A. Ramani	12
+	Ordinary Differential Equations	2017	John M. Stewart	12
+ PDF Chat	Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations	2000	Satoshi Fukutani Kazuo Okamoto Hiroshi Umemura	12
+ PDF Chat	Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes	1910	Bertrand Gambier	12
+ PDF Chat	Remarks on the Yablonskii-Vorob’ev polynomials	2000	Makoto Taneda	12
+ PDF Chat	Symmetry reductions and exact solutions of a class of nonlinear heat equations	1994	Peter A. Clarkson Elizabeth L. Mansfield	12
+	Group Analysis of Differential Equations.	1985	Willard Miller Л.В. Овсянников	12
+	Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree	1993	Christoper M. Cosgrove George Scoufis	12
+	New similarity solutions for the modified Boussinesq equation	1989	Peter A. Clarkson	12
+	Solitons and rational solutions of nonlinear evolution equations	1978	Mark J. Ablowitz Junkichi Satsuma	11
+	Automatically determining symmetries of partial differential equations	1985	Fritz Schwarz	11