Location: School of Mathematics, Statistics and Actuarial
Science, Cornwallis Building, Room E.104
Position: Professor of Mathematics and Interim Head of School
Email: P.A.Clarkson@kent.ac.uk
smsasHoS@kent.ac.uk
Phone: +44 (0) 1227 827781
Mobile: +44 (0) 7790 504215
Fax: +44 (0) 1227 827932
Postal Address: School of Mathematics, Statistics and
Actuarial Science,
University of Kent,
Canterbury, Kent,
CT2 7NF,
United Kingdom.
MA593 Topics in Modern Applied Mathematics
MA871 Asymptotics and Perturbation Methods
 Soliton theory, in particular the Painlevé equations, and Painlevé analysis.
 Asymptotics, Bäcklund transformations, connection formulae and exact solutions for nonlinear ordinary differential and difference equations, in
particular the Painlevé equations.
 Orthogonal polynomials and special functions, in particular nonlinear special functions such as the Painlevé equations.
 Symmetry reductions and exact solutions of nonlinear partial differential equations, in particular using nonclassical and generalized techniques.
 I am a member of the SIAM Activity Group on Orthogonal
Polynomials and Special Functions. During recent years I have served as an
Officer of the Activity Group: Secretary (20022004, 20112013), Chair (20052007)
and ViceChair (20082010).
 The activity group promotes basic research in orthogonal polynomials and
special functions; furthers the application of this subject in other parts of
mathematics, and in science and industry; and encourages and supports the
exchange of information, ideas, and techniques between workers in this field
and other mathematicians and scientists.
 The activity group publishes the electronic newsletter OPSF NET,
maintains an electronic discussion group (OPSFtalk), sponsors minisymposia
at the SIAM annual meeting, and maintains a
web site which includes a conference calendar,
a member directory, and an electronic mailing list. The activity group also awards the
Gábor Szegö Prize every two years to an earlycareer researcher for outstanding research
contributions in the area of orthogonal polynomials and special functions.

Nonlinear Guided Waves VII, Kingussie, Scotland (79 May 2014).

SIAM Conference on Nonlinear Waves and Coherent Structures, Churchill College, Cambridge (1114 August 2014).

Exceptional orthogonal polynomials and exact solutions in Mathematical Physics, Segovia, Spain (712 September 2014).

Conference on Mathematics and its Applications, Kuwait (1417 November 2014).

Foundations of Computational Mathematics, Montevideo, Uruguay (1120 December 2014).
Organizer of workshop on Orthogonal Polynomials and Special Functions

Modern Applications of Complex Variables: Modeling, Theory and Computation, Banff, Canada (1116 January 2015).
 8th International Conference on Industrial and Applied Mathematics (ICIAM 2015),
Beijing, China (1014 August 2015).
Books
 M J Ablowitz and P A Clarkson,
Solitons, Nonlinear Evolution Equations and Inverse Scattering, London
Mathematical Society Lecture Note Series vol. 149, Cambridge University Press, Cambridge
(1991).
 J A Tuszynski, J M Dixon and P A Clarkson, From Nonlinearity to
Coherence: Universal features of nonlinear behaviour in manybody
physics, Oxford University Press,
Oxford (1997).
Edited Volumes
 P A Clarkson (Editor),
Applications of Analytic and Geometric Methods to Nonlinear Differential
Equations, NATO Advanced Study Institute Series C: Mathematical and
Physical Sciences, vol. 413, Kluwer, Dordrecht (1993).
 P A Clarkson and F W Nijhoff (Editors),
Symmetries and Integrability of Difference Equations, London
Mathematical Society Lecture Note Series vol. 255, Cambridge University Press, Cambridge
(1999).
 M J Ablowitz and P A Clarkson (Editors), Solitons and Symmetries,
Special issue of
Journal of Engineering Mathematics, Kluwer, Dordrecht, vol.
36, issue 1/2 (1999).
 P A Clarkson, N Joshi, M Mazzocco, F W Nijhoff and M Noumi (Editors),
One hundred years of PVI, the FuchsPainlevé equation,
Special issue of Journal of Physics A:
Mathematical & General, Institute of Physics, Bristol, vol.
39, issue 39 (2006).
Papers
 P A Clarkson and J B McLeod, "A note on solutions of Painlevé
II", Physics
Letters A92 (1982) pp 425426.
 P A Clarkson, "The Painlevé property and a partial differential
equation with an essential singularity", Physics
Letters A109 (1985) pp 205208.
 P A Clarkson, "Remarks on the twodimensional SineGordon equation and
the Painlevé tests", Letters in
Mathematical Physics 10 (1986) pp 297299.
 P A Clarkson, "The Painlevé property, a modified Boussinesq equation
and a modified KadomtsevPetviashvili equation", Physica
D19 (1986) pp 447450.
 P A Clarkson, J B McLeod, P J Olver and A Ramani, "Integrability of
KleinGordon equations", SIAM Journal of
Mathematical Analysis 17 (1986) pp 798802.
 P A Clarkson, R J LeVeque and R Saxton, "Solitary wave interactions in
elastic rods", Studies
in Applied Mathematics 75 (1986) pp 95121.
 P A Clarkson and C M Cosgrove, "The Painlevé property and a
generalised derivative Schrödinger equation", Journal of Physics A:
Mathematical & General 20 (1987) pp 20032024.
 P A Clarkson, "Painlevé analysis for the damped, driven nonlinear
Schrödinger equation", Proceedings
of the Royal Society of Edinburgh 109A (1988) pp 109126.
 P A Clarkson and J B McLeod, "A connection formula for the second
Painlevé transcendent",
Archive for Rational Mechanics and Analysis 103 (1988) pp
97138.
 P A Clarkson, "New similarity solutions of the modified Boussinesq
equation", Journal of
Physics A: Mathematical & General 22 (1989) pp 23552367.
 P A Clarkson, A S Fokas and M J Ablowitz, "Hodograph transformations on
linearizable partial differential equations", SIAM Journal of
Applied Mathematics 49 (1989) pp 11881209.
 P A Clarkson, "New similarity solutions and Painlevé analysis for
the symmetric regularized long wave and the modified BenjaminBonaMahoney
equations", Journal of
Physics A: Mathematical & General 22 (1989) pp 38213848.
 P A Clarkson and M D Kruskal, "New similarity solutions of the Boussinesq
equation", Journal of Mathematical
Physics 30 (1989) pp 22012213.
 P A Clarkson, "Painlevé analysis and the complete integrability of a
generalized variablecoefficient KadomtsevPetviashvili equation", IMA
Journal of Applied Mathematics 44 (1990) pp 2753.
 S Chakravarty, M J Ablowitz and P A Clarkson, "Reductions of selfdual
YangMills fields and classical systems", Physical Review Letters 65 (1990)
pp 10851087.
 P A Clarkson, "New exact solutions of the Boussinesq equation", European
Journal of Applied Mathematics 1 (1990) pp 279300.
 P A Clarkson and J A Tuszynski, "Exact solutions of multidimensional
derivative nonlinear Schrödinger equations for manybody systems at
criticality", Journal of
Physics A: Mathematics & General 23 (1990) pp 42694288.
 P A Clarkson and P Winternitz, "Nonclassical symmetry reductions for the
KadomtsevPetviashvili equation", Physica
D49 (1991) pp 257272.
 M D Kruskal and P A Clarkson, "The PainlevéKowalevski and
polyPainlevé tests for integrability", Studies
in Applied Mathematics 86 (1992) pp 87165.
 P A Clarkson, "Nonclassical similarity reductions and exact solutions of
a generalized nonlinear Schrödinger equation", Nonlinearity 5
(1992) pp 453472.
 A P Bassom, P A Clarkson, A C Hicks and J B McLeod, "Integral equations
and exact solutions for the fourth Painlevé equation", Proceedings
of the Royal Society of London Series A: Mathematical, Physical and
Engineering Sciences 437 (1992) pp 124.
 M C Nucci and P A Clarkson, "The nonclassical method is more general than
the direct method for symmetry reductions: an example of the FitzhughNagumo
equation", Physics
Letters 164A (1992) pp 4956.
 P A Clarkson and S Hood, "Nonclassical symmetry reductions of the
ZabalotskayaKhoklov equation", European
Journal of Applied Mathematics 3 (1992) pp 381414.
 P A Clarkson and S Hood, "Symmetry reductions of a cylindrical nonlinear
Schrödinger equation", Journal of Physics A:
Mathematics & General 26 (1993) pp 133150.
 A P Bassom, P A Clarkson and A C Hicks, "Numerical studies of the fourth
Painlevé equation", IMA
Journal of Applied Mathematics 50 (1993) pp 167193.
 P A Clarkson, "Nonclassical symmetry reductions of nonlinear partial
differential equations", Mathematical
and Computer Modelling 18 Issue 10 (1993) pp 4568.
 P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of a class of nonlinear heat equations", Physica
D70 (1994) pp 250288.
 P A Clarkson and S Hood, "New symmetry reductions and exact solutions of
the DaveyStewartson equation. I. Reductions to ordinary differential
equations", Journal of Mathematical
Physics 35 (1994) pp 255283.
 P A Clarkson and E L Mansfield, "On a shallow water wave equation", Nonlinearity 7
(1994) pp 9751000.
 P A Clarkson and D K Ludlow, "Symmetry reductions, exact solutions and
Painlevé analysis of a generalized Boussinesq equation", Journal of
Mathematical Analysis and Applications 186 (1994) pp 132155.
 A P Bassom and P A Clarkson, "New exact solutions of the discrete fourth
Painlevé equation", Physics
Letters A194 (1994) pp 358370.
 P A Clarkson and E L Mansfield, "Algorithms for the nonclassical method
of symmetry reductions", SIAM Journal of
Applied Mathematics 54 (1994) pp 16931719.
 A P Bassom, P A Clarkson and A C Hicks, "Bäcklund transformations
and solution hierarchies for the fourth Painlevé equation", Studies
in Applied Mathematics 95 (1995) pp 171.
 XB Hu and P A Clarkson, "Rational solutions of a differentialdifference
KdV equation, the Toda equation and the discrete KdV equation", Journal of Physics A:
Mathematical and General 28 (1995) pp 50095016.
 P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of shallow water wave equations", Acta Applicandae
Mathematicae 39 (1995) pp 245276.
 P A Clarkson, "Nonclassical symmetry reductions for the Boussinesq
equation", Chaos,
Solitons & Fractals 5 (1995) pp 22612301.
 P A Clarkson and P J Olver, "Symmetry and the Chazy equation", Journal of
Differential Equations 124 (1996) pp 225246.
 A P Bassom, P A Clarkson and A C Hicks, "On the application of solution
hierarchies of the fourth Painlevé equation to several physically
significant nonlinear partial differential equations", Advances in Differential
Equations 1 (1996) pp 175198.
 P A Clarkson, E L Mansfield and A E Milne, "Symmetries and exact
solutions of a 2+1dimensional SineGordon system", Philosophical
Transactions of the Royal Society of London A: Physical Science and
Engineering 354 (1996) pp 18071835.
 E L Mansfield and P A Clarkson, "Symmetries and exact solutions for a
2+1dimensional shallow water wave equation", Mathematics
and Computers in Simulation 43 (1997) pp 3955.
 A E Milne, P A Clarkson and A P Bassom, "Bäcklund transformations
and solution hierarchies for the third Painlevé equation", Studies
in Applied Mathematics 98 (1997) pp 139194.
 A E Milne, P A Clarkson and A P Bassom, "Application of the isomonodromy
deformation method to the fourth Painlevé equation", Inverse Problems 13
(1997) pp 421439.
 E L Mansfield and P A Clarkson, "Applications of the differential algebra
package diffgrob2 to classical symmetries of PDEs", Journal of
Symbolic Computation 23 (1997) pp 517533.
 P A Clarkson, E L Mansfield and T J Priestley, "Symmetries of a class of
nonlinear third order partial differential equations", Mathematical
and Computer Modelling 25 Issues 89 (1997) pp 195212.
 XB Hu, P A Clarkson and R K Bullough, "New integrable
differentialdifference systems", Journal of Physics A:
Mathematical and General 30 (1997) pp L669L676.
 P A Clarkson, P R Gordoa and A Pickering, "Multicomponent equations
associated to nonisospectral scattering problems", Inverse Problems 13
(1997) pp 14631476.
 P A Clarkson, D K Ludlow and T J Priestley, "The classical, direct and
nonclassical methods for symmetry reductions of nonlinear partial differential
equations", Methods and
Applications of Analysis 4 (1997) pp 173195.
 XB Hu and P A Clarkson, "Bäcklund transformations and nonlinear
superposition formulae of a differentialdifference KdV equation", Journal of Physics A:
Mathematical and General 31 (1998) pp 14051414.
 D K Ludlow, P A Clarkson and A P Bassom, "Nonclassical symmetry
reductions of the threedimensional incompressible NavierStokes equations"
Journal of Physics A:
Mathematical and General 31 (1998) pp 79657980.
 A P Bassom, P A Clarkson, C K Law and J B McLeod, "Application of uniform
asymptotics to the second Painlevé transcendent",
Archive for Rational Mechanics and Analysis 143 (1998) pp
241271.
 P A Clarkson and T J Priestley, "Shallow water wave systems", Studies
in Applied Mathematics 101 (1998) pp 389432.
 E L Mansfield, G J Reid and P A Clarkson, "Nonclassical reductions of a
coupled nonlinear Schrödinger system", Computer
Physics Communications 115 (1998) pp 460488.
 P A Clarkson and T J Priestley, "Symmetries of a class of nonlinear
fourth order partial differential equations", Journal of Nonlinear Mathematical
Physics 6 (1999) pp 6698.
 P A Clarkson, N Joshi and A Pickering, "Bäcklund transformations for
the second Painlevé hierarchy: a modified truncation approach", Inverse Problems 15
(1999) pp 175187.
 M J Ablowitz and P A Clarkson, "Solitons and symmetries", Journal
of Engineering Mathematics 36 (1999) pp 19.
 D K Ludlow, P A Clarkson and A P Bassom, "Nonclassical symmetry
reductions of the twodimensional incompressible NavierStokes equations", Studies
in Applied Mathematics 103 (1999) pp 183240.
 P A Clarkson and H N Webster, "Hierarchies of exact solutions of the
discrete third Painlevé equation", Chaos,
Solitons & Fractals 11 (2000) pp 5371.
 P A Clarkson, E L Mansfield and H N Webster, "On the relationship between
the discrete and continuous Painlevé equations", Theoretical
& Mathematical Physics 122 (2000) pp 116.
 D K Ludlow, P A Clarkson, and A P Bassom, "New similarity solutions of
the unsteady incompressible boundarlayer equations", Quarterly Journal of Mechanics and
Applied Mathematics 53 (2000) pp 175206.
 M S Bruzon, P A Clarkson, M L Gandarias and E Medina, "Symmetry
reductions of a model for turbulance", Journal of Physics A:
Mathematical and General 34 (2001) pp 37513760.
 X B Hu and P A Clarkson, "Rational solutions of an extended
LotkaVolterra equation", Journal of Nonlinear Mathematical
Physics 9, Supp. 1 (2002) pp 7586.
 P A Clarkson, "Painlevé equations  nonlinear special functions", Journal of
Computational and Applied Mathematics 153 (2003) pp 127140.
 P A Clarkson and E L Mansfield, "The second Painlevé equation, its
hierarchy and associated special polynomials", Nonlinearity 16
(2003) pp R1R26.
 P A Clarkson, "The third Painlevé equation and associated special
polynomials", Journal of
Physics A: Mathematical and General 36 (2003) pp 95079532.
 P A Clarkson, "The fourth Painlevé equation and associated special
polynomials", Journal of Mathematical
Physics 44 (2003) pp 53505374.
 P A Clarkson, A N W Hone and N Joshi, "Hierarchies of difference
equations and Bäcklund transformations", Journal of Nonlinear Mathematical
Physics 10, Supp. 2 (2003) pp 1326.
 P A Clarkson, "Remarks on the YablonskiiVorob'ev polynomials", Physics
Letters A319 (2003) pp 137144.
 P A Clarkson and G V Filipuk, "Symmetric hierarchy of the fourth
Painlevé equation", Proceedings of Institute of Mathematics of
Minsk 12 (2004) pp 8286.
 P A Clarkson, "Special polynomials associated with rational solutions of
the fifth Painlevé equation", Journal of
Computational and Applied Mathematics 178 (2005) pp 111129.
 A Sen, A N W Hone and P A Clarkson, "Darboux transformations and the
symmetric fourth Painlevé equation", Journal of Physics A:
Mathematical and General 38 (2005) pp 97519764.
 N Bila, E L Mansfield and P A Clarkson, "Symmetry
group analysis of the shallow water and semigeostrophic systems", Quarterly Journal of Mechanics and
Applied Mathematics 59 (2006) pp 95123.
 P A Clarkson, "Special polynomials associated with rational solutions of
the Painlevé equations and applications to soliton equations", Computational Methods and
Function Theory 6 (2006) pp 329401.
 P A Clarkson, N Joshi, M Mazzocco, F W Nijhoff and M Noumi,
"One hundred years of PVI, the FuchsPainlevé equation", Journal of Physics A:
Mathematical & General 39 (2006) Preface.
 P A Clarkson, "Special polynomials associated with rational solutions of
the defocusing nonlinear Schrödinger equation and the fourth Painlevé
equation",
European Journal of Applied Mathematics 17 (2006) pp 293322.
 S E Harris and P A Clarkson,
"Painlevé analysis and similarity reductions for the magma
equations",
Symmetry, Integrability and Geometry: Methods and Applications
2 (2006) 068 (17 pages).
 A Sen, A N W Hone and P A Clarkson,
"On the Lax pairs of symmetric Painlevé equations", Studies
in Applied Mathematics 117 (2006) pp 299319.
 G V Filipuk and P A Clarkson,
"The symmetric fourth Painlevé hierarchy and associated special polynomials", Studies
in Applied Mathematics 121 (2008) pp 157188.
 P A Clarkson, "Rational solutions of the Boussinesq equation", Analysis and Applications 6 (2008) pp 349369.
 P A Clarkson, "Vortices and polynomials", Studies
in Applied Mathematics 123 (2009) pp 3762.
 P A Clarkson, "Rational solutions of the classical Boussinesq system", Nonlinear Analysis: Real World Applications 10 (2009) pp 33603371.
 A Ankiewicz, P A Clarkson and N Akhmediev, "Rogue waves, rational solutions, the patterns of their zeros and integral relations", Journal of Physics A:
Mathematical and Theoretical 43 (2010) 122002 (9 pages).
 P A Clarkson, "Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations", Journal of Physics A: Mathematical and Theoretical
46 (2013) 185205 (18 pages).
 P A Clarkson and K Jordaan,
"The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation",
Constructive Approximation 39 (2014) 223254.
[DOI:10.1007/s0036501392204]
Chapters in Books
 S Chakravarty, M J Ablowitz and P A Clarkson, "One dimensional reductions
of selfdual YangMills fields and classical systems", in Recent
Advances in General Relativity: Essays in Honor of Ted Newman [Editors
A I Janis and J R Porter], Birkhäuser Boston, Basel (1992) pp 6071.
 P A Clarkson, "Painlevé equations and associated polynomials", in
Theory and Applications of Special Functions. A volume dedicated to Mizan
Rahman [Editors Mourad E H Ismail and Erik Koelink], Developments in
Mathematics, vol. 13, SpringerVerlag, Berlin (2005) pp 123163.
 P A Clarkson, "Painlevé Transcendents", in
NIST Handbook of Mathematical Functions [Editors F W J Olver, D W Lozier, R F Boisvert and C W Clark], Cambridge University Press, Cambridge (2010) pp 723740.
Papers in Conference Proceedings
 P A Clarkson and J B McLeod, "A connection formula for the second
Painlevé transcendent", in Ordinary and Partial Differential
Equations [Editors W N Everitt and B D Sleeman], Lecture
Notes in Mathematics vol. 964, SpringerVerlag, Berlin (1983) pp
135142.
 P A Clarkson, "The Painlevé conjecture, the Painlevé property
for partial differential equations and complete integrability", in
Solitons and Coherent Structures [Editors D K Campbell, A C Newell, R J
Schrieffer and H Segur], Physica
D18 (1986) pp 209210.
 P A Clarkson, "New similarity reductions of Boussinesqtype equations",
in Partially
Integrable Nonlinear Evolution Equations and their Physical
Applications [Editors R Conte and N Boccara], NATO Advanced Study
Institute Series C: Mathematical and Physical Sciences, vol. 310,
Kluwer, Dordrecht (1990) pp 575576.
 P A Clarkson, "Examples of nonclassical similarity reductions", in
Nonlinear Evolution Equations and Dynamical Systems [Editors S Carillo
and O Ragnisco], Research Reports in Physics (Nonlinear Dynamics),
SpringerVerlag, BerlinHeidelberg (1990) pp 4245.
 P A Clarkson, "Nonclassical symmetry reductions and exact solutions for
physically significant nonlinear evolution equations", in Nonlinear and
Chaotic Phenomena [Editors W Rozmus and J A Tuszynski], World Scientific,
Singapore (1991) pp 7279.
 P A Clarkson, "Nonclassical symmetry reductions of a generalized
nonlinear Schrödinger equation", in Solitons and Chaos [Editors I
Antoniou and F Lambert], Research Reports in Physics (Nonlinear Dynamics),
SpringerVerlag, Berlin (1991) pp 246254.
 P A Clarkson and J B McLeod, "Integral equations and connection formulae
for the Painlevé equations", in Painlevé Transcendents, their
Asymptotics and Physical Applications [Editors P Winternitz and D Levi],
NATO Advanced Study Institute Series B: Physics, vol. 278, Plenum, New
York (1992) pp 131.
 P A Clarkson and E L Mansfield, "Nonclassical symmetry reductions and
exact solutions of nonlinear reactiondiffusion equations", in Applications of Analytic
and Geometric Methods to Nonlinear Differential Equations [Editor P A
Clarkson], NATO Advanced Study Institute Series C: Mathematical and Physical
Sciences, vol. 413, Kluwer, Dordrecht (1993) pp 375389.
 A C Hicks, P A Clarkson and A P Bassom, "A study of the fourth
Painlevé equation", in Applications of Analytic
and Geometric Methods to Nonlinear Differential Equations [Editor P A
Clarkson], NATO Advanced Study Institute Series C: Mathematical and Physical
Sciences, vol. 413, Kluwer, Dordrecht (1993) pp 315330.
 S Hood and P A Clarkson, "Symmetry reductions of the DaveyStewartson
system", in Applications of Analytic and
Geometric Methods to Nonlinear Differential Equations [Editor P A
Clarkson], NATO Advanced Study Institute Series C: Mathematical and Physical
Sciences, vol. 413, Kluwer, Dordrecht (1993) pp 395404.
 D K Ludlow and P A Clarkson, "Symmetry reductions and exact solutions for
a generalized Boussinesq equation", in Applications of Analytic and
Geometric Methods to Nonlinear Differential Equations [Editor P A
Clarkson], NATO Advanced Study Institute Series C: Mathematical and Physical
Sciences, vol. 413, Kluwer, Dordrecht (1993) pp 415430.
 A E Milne and P A Clarkson, "Rational solutions and Bäcklund
transformations for the third Painlevé equation", in Applications of Analytic and
Geometric Methods to Nonlinear Differential Equations [Editor P A
Clarkson], NATO Advanced Study Institute Series C: Mathematical and Physical
Sciences, vol. 413, Kluwer, Dordrecht (1993) pp 341352.
 P A Clarkson and E L Mansfield, "Symmetries of the nonlinear heat
equation", in
Modern Group Analysis: Advanced Analytical and Computational Methods in
Mathematical Physics [Editors N H Ibragimov, M Torrisi and A Valenti],
Kluwer, Dordrecht (1993) pp 155171.
 P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of a shallow water wave equation", in Fourteenth IMACS World Congress on
Computational and Applied Mathematics [Editor W F Ames], 1994, vol.
1, IMACS (1994) pp 97101.
 E L Mansfield and P A Clarkson, "Applications of the differential algebra
package diffgrob2 to reductions of PDE", in Fourteenth IMACS
World Congress on Computational and Applied Mathematics [Editor W F Ames],
vol. 1, IMACS (1994) pp 336339.
 P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of shallow water wave equations", in Proceedings of the Conference on
Nonlinear Coherent Structures in Physics and Biology [Editors D B Duncan
and J C Eilbeck], published on WWW (1995).
 T J Priestley and P A Clarkson, "On a shallow water wave system", in
Proceedings of the Conference on Nonlinear Coherent Structures in Physics
and Biology [Editors D B Duncan and J C Eilbeck], published on WWW (1995).
 P A Clarkson, E L Mansfield and S B Townley, "Symmetries for nonlinear
diffusion equations with forcing feedback", in Third European Control
Conference (1995) pp 29112916.
 P A Clarkson and A P Bassom, "Bäcklund transformations and
hierarchies of exact solutions for the fourth Painlevé equation and their
application to discrete equations", in Symmetries and
Integrability of Difference Equations [Editors D Levi, L Vinet and P
Winternitz], Centre de Recherches Mathématiques Proceedings and Lecture
Notes Series, vol. 9, American Mathematical Society, Providence, RI
(1996) pp 6377.
 XB Hu and P A Clarkson, "Bäcklund transformation and new explicit
solutions of the twodimensional Toda equation", in
Symmetries and Integrability of Difference Equations II [Editors P
A Clarkson and F W Nijhoff], London Mathematical Society Lecture Note Series,
vol. 255, Cambridge University Press, Cambridge (1999) pp 1522.
 P A Clarkson, "The Chazy equation", in
Modern Group Analysis: Developments in theory computation and
application [Editors N H Ibragimov, K R Naqvi and E Straume], MARS
Publishers, Trondheim, Norway (1999) pp 7989.
 P A Clarkson and P Winternitz, "Symmetry reduction and exact solutions of
nonlinear partial differential equations", in
The Painlevé Property, One Century Later [Editor, R Conte],
CRM Series in Mathematical Physics, SpringerVerlag, New York (1999) pp
591660.
 P G Estévez and P A Clarkson, "Discrete equations and the singular
manifold method", in Symmetries and
Integrability of Difference Equations III [Editors D Levi and P
Winternitz], Centre de Recherches Mathématiques Proceedings and Lecture
Notes Series, vol. 25, American Mathematical Society, Providence, RI
(2000) pp 139146.
 P A Clarkson, E L Mansfield and H N Webster, "On discrete Painlevé
equations as Bäcklund transformations", in Bäcklund and
Darboux Transformations [Editors D Levi and P Winternitz], Centre de
Recherches Mathématiques Proceedings and Lecture Notes Series, vol.
29, American Mathematical Society, Providence, RI (2001) pp
129139.
 P A Clarkson and E L Mansfield, "Open problems in symmetry analysis",
in Geometrical Study
of Differential Equations [Editors J A Leslie and T Robart],
Contemporary Mathematics Series, vol. 285, American Mathematical
Society, Providence, RI (2001) pp 195205.
 P A Clarkson and C M Cosgrove, "Symmetry, the Chazy equation and Chazy
hierarchies", in
Isomondromic Deformations and Applications in Physics [Editors J
Harnad and A R Its], Centre de Recherches Mathématiques Proceedings and
Lecture Notes Series, vol. 31, American Mathematical Society,
Providence, RI (2002) pp 113129.
 P A Clarkson, "Rational solutions of the fourth Painlevé equation and
the nonlinear Schrödinger equation", in Group Analysis
of Differential Equations, [Editors N H Ibragimov, C Sophocleous and P
A Damianou], proceedings of the 10th International Conference in MOdern GRoup
ANalysis (2005) pp 4757.
 P A Clarkson, "On rational solutions of the fourth Painlevé equation and its Hamiltonian",
in Group Theory and
Numerical Analysis [Editors P Winternitz, D GomezUllate, A Iserles, D
Levi, P J Olver, R Quispel and P Tempesta], Centre de Recherches
Mathématiques Proceedings and Lecture Notes Series, vol. 39,
American Mathematical Society, Providence, RI (2005) pp 103118.
 P A Clarkson, "Painlevé equations  nonlinear special functions", in
Orthogonal Polynomials and Special Functions: Computation and
Application [Editors F Márcellan and W van Assche], Lecture
Notes in Mathematics, vol. 1883, SpringerVerlag, Berlin (2006) pp
331411.
 P A Clarkson, "Special polynomials associated with rational and algebraic
solutions of the Painlevé equations", in
Théories Asymptotiques et Equations de Painlevé
[Editors E Delabaere and M LodayRichaud], Séminaires et Congrès, vol. 14,
Sociètè Mathèmatique de France, Paris
(2007) pp 2152.
 P A Clarkson, N Joshi and M Mazzocco "The Lax pair for the mKdV hierarchy", in
Théories Asymptotiques et Equations de Painlevé
[Editors E Delabaere and M LodayRichaud], Séminaires et Congrès, vol. 14,
Sociètè Mathèmatique de France, Paris
(2007) pp 5364.
 P A Clarkson "Asymptotics of the second Painlevé equation" in
Special Functions and Orthogonal Polynomials [Editors Diego Dominici and Robert S Maier], Contemporary Mathematics Series, vol. 471, American Mathematical Society, Providence, RI (2008) pp 6984.
 P A Clarkson and B W M Thomas,
Special polynomials and exact solutions of the dispersive water wave and modified Boussinesq equations in Group Analysis of Differential Equations and Integrable Systems [Editors N Ivanova, C Sophocleous, R Popovych, P Damianou and A Nikitin], Proceedings of the Fourth Workshop (2009) pp 6276.
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