- 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 Women in Mathematics Committee
of the London Mathematical Society.

- I am chair of the steering committee for the Good Practice Scheme which has the the aim of supporting Mathematics departments interested in embedding equal opportunities for women within their working practices.
The Scheme provides specific support for departments working towards Athena SWAN Award status
and organizes events.

- The London Mathematical Society launched its report
Advancing women in mathematics: good practice in UK university departments at the House of Commons on 27th February 2013.
More details of the launch and the report are given
here.

- I am participant in the NIST Digital Library
of Mathematical Functions project, companion to the
NIST Handbook of Mathematical Functions, funded by the U.S. National Science
Foundation, and organised by the National Institute of Standards and
Technology, Gaithersburg, Maryland, USA. This project is to update Abramowitz
and Stegun's
*Handbook of Mathematical Functions*. My role in the project is writing the chapter on Painlevé Transcendents.

- 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 (2002-2004, 2011-2013), Chair (2005-2007)
and Vice-Chair (2008-2010).

- 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 OP-SF 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 early-career researcher for outstanding research
contributions in the area of orthogonal polynomials and special functions.

- IMA Mathematics 2016, London (17 March 2016)

- 40th Symposium of Numerical and Applied Mathematics (SANUM), Stellenbosch, South Africa (22-24 March 2016)

- Nonlinear Waves - Theory and Applications, Beijing, China (25-28 June 2016)

- Symmetries and Integrability of Difference Equations (SIDE12), Sainte-Adèle, Québec, Canada (3-9 July 2016)

- SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, USA (8-11 August 2016)

- Acta Applicandae Mathematicae

- EqWorld: The World of Mathematical Equations

- European Journal of Applied Mathematics

- Quarterly Journal of Mechanics and Applied Mathematics

- Studies in Applied Mathematics

- Symmetry, Integrability and Geometry: Methods and Applications

- P A Clarkson, A F Loureiro and W Van Assche, Unique positive solution for an alternative discrete Painlevé I equation, arXiv:1508.04916 [nlin.SI].
- P A Clarkson, K Jordaan and A Kelil, A generalized Freud weight, arXiv:1510.03772 [math.CA].
- P A Clarkson, On Airy Solutions of the Second Painlevé Equation, arXiv:arXiv:1510.08326 [nlin.SI].

- 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 Non-linearity to Coherence: Universal features of nonlinear behaviour in many-body physics*, Oxford University Press, Oxford (1997).

- 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 Fuchs-Painlevé equation*, Special issue of*Journal of Physics A: Mathematical & General*, Institute of Physics, Bristol, vol.**39**, issue 39 (2006).

- P A Clarkson and J B McLeod, "A note on solutions of Painlevé
II",
*Physics Letters***A92**(1982) pp 425-426. - P A Clarkson, "The Painlevé property and a partial differential
equation with an essential singularity",
*Physics Letters***A109**(1985) pp 205-208. - P A Clarkson, "Remarks on the two-dimensional Sine-Gordon equation and
the Painlevé tests",
*Letters in Mathematical Physics***10**(1986) pp 297-299. - P A Clarkson, "The Painlevé property, a modified Boussinesq equation
and a modified Kadomtsev-Petviashvili equation",
*Physica***D19**(1986) pp 447-450. - P A Clarkson, J B McLeod, P J Olver and A Ramani, "Integrability of
Klein-Gordon equations",
*SIAM Journal of Mathematical Analysis***17**(1986) pp 798-802. - P A Clarkson, R J LeVeque and R Saxton, "Solitary wave interactions in
elastic rods",
*Studies in Applied Mathematics***75**(1986) pp 95-121. - 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 2003-2024. - P A Clarkson, "Painlevé analysis for the damped, driven nonlinear
Schrödinger equation",
*Proceedings of the Royal Society of Edinburgh***109A**(1988) pp 109-126. - P A Clarkson and J B McLeod, "A connection formula for the second
Painlevé transcendent",
*Archive for Rational Mechanics and Analysis***103**(1988) pp 97-138. - P A Clarkson, "New similarity solutions of the modified Boussinesq
equation",
*Journal of Physics A: Mathematical & General***22**(1989) pp 2355-2367. - 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 1188-1209. - P A Clarkson, "New similarity solutions and Painlevé analysis for
the symmetric regularized long wave and the modified Benjamin-Bona-Mahoney
equations",
*Journal of Physics A: Mathematical & General***22**(1989) pp 3821-3848. - P A Clarkson and M D Kruskal, "New similarity solutions of the Boussinesq
equation",
*Journal of Mathematical Physics***30**(1989) pp 2201-2213. - P A Clarkson, "Painlevé analysis and the complete integrability of a
generalized variable-coefficient Kadomtsev-Petviashvili equation",
*IMA Journal of Applied Mathematics***44**(1990) pp 27-53. - S Chakravarty, M J Ablowitz and P A Clarkson, "Reductions of self-dual
Yang-Mills fields and classical systems",
*Physical Review Letters***65**(1990) pp 1085-1087. - P A Clarkson, "New exact solutions of the Boussinesq equation",
*European Journal of Applied Mathematics***1**(1990) pp 279-300. - P A Clarkson and J A Tuszynski, "Exact solutions of multidimensional
derivative nonlinear Schrödinger equations for many-body systems at
criticality",
*Journal of Physics A: Mathematics & General***23**(1990) pp 4269-4288. - P A Clarkson and P Winternitz, "Nonclassical symmetry reductions for the
Kadomtsev-Petviashvili equation",
*Physica***D49**(1991) pp 257-272. - M D Kruskal and P A Clarkson, "The Painlevé-Kowalevski and
poly-Painlevé tests for integrability",
*Studies in Applied Mathematics***86**(1992) pp 87-165. - P A Clarkson, "Nonclassical similarity reductions and exact solutions of
a generalized nonlinear Schrödinger equation",
*Nonlinearity***5**(1992) pp 453-472. - 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 1-24. - M C Nucci and P A Clarkson, "The nonclassical method is more general than
the direct method for symmetry reductions: an example of the Fitzhugh-Nagumo
equation",
*Physics Letters***164A**(1992) pp 49-56. - P A Clarkson and S Hood, "Nonclassical symmetry reductions of the
Zabalotskaya-Khoklov equation",
*European Journal of Applied Mathematics***3**(1992) pp 381-414. - P A Clarkson and S Hood, "Symmetry reductions of a cylindrical nonlinear
Schrödinger equation",
*Journal of Physics A: Mathematics & General***26**(1993) pp 133-150. - 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 167-193. - P A Clarkson, "Nonclassical symmetry reductions of nonlinear partial
differential equations",
*Mathematical and Computer Modelling***18**Issue 10 (1993) pp 45-68. - P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of a class of nonlinear heat equations",
*Physica***D70**(1994) pp 250-288. - P A Clarkson and S Hood, "New symmetry reductions and exact solutions of
the Davey-Stewartson equation. I. Reductions to ordinary differential
equations",
*Journal of Mathematical Physics***35**(1994) pp 255-283. - P A Clarkson and E L Mansfield, "On a shallow water wave equation",
*Nonlinearity***7**(1994) pp 975-1000. - 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 132-155. - A P Bassom and P A Clarkson, "New exact solutions of the discrete fourth
Painlevé equation",
*Physics Letters***A194**(1994) pp 358-370. - P A Clarkson and E L Mansfield, "Algorithms for the nonclassical method
of symmetry reductions",
*SIAM Journal of Applied Mathematics***54**(1994) pp 1693-1719. - 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 1-71. - X-B Hu and P A Clarkson, "Rational solutions of a differential-difference
KdV equation, the Toda equation and the discrete KdV equation",
*Journal of Physics A: Mathematical and General***28**(1995) pp 5009-5016. - P A Clarkson and E L Mansfield, "Symmetry reductions and exact solutions
of shallow water wave equations",
*Acta Applicandae Mathematicae***39**(1995) pp 245-276. - P A Clarkson, "Nonclassical symmetry reductions for the Boussinesq
equation",
*Chaos, Solitons & Fractals***5**(1995) pp 2261-2301. - P A Clarkson and P J Olver, "Symmetry and the Chazy equation",
*Journal of Differential Equations***124**(1996) pp 225-246. - 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 175-198. - P A Clarkson, E L Mansfield and A E Milne, "Symmetries and exact
solutions of a 2+1-dimensional Sine-Gordon system",
*Philosophical Transactions of the Royal Society of London A: Physical Science and Engineering***354**(1996) pp 1807-1835. - E L Mansfield and P A Clarkson, "Symmetries and exact solutions for a
2+1-dimensional shallow water wave equation",
*Mathematics and Computers in Simulation***43**(1997) pp 39-55. - 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 139-194. - 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 421-439. - 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 517-533. - 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 8-9 (1997) pp 195-212. - X-B Hu, P A Clarkson and R K Bullough, "New integrable
differential-difference systems",
*Journal of Physics A: Mathematical and General***30**(1997) pp L669-L676. - P A Clarkson, P R Gordoa and A Pickering, "Multi-component equations
associated to non-isospectral scattering problems",
*Inverse Problems***13**(1997) pp 1463-1476. - 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 173-195. - X-B Hu and P A Clarkson, "Bäcklund transformations and nonlinear
superposition formulae of a differential-difference KdV equation",
*Journal of Physics A: Mathematical and General***31**(1998) pp 1405-1414. - D K Ludlow, P A Clarkson and A P Bassom, "Nonclassical symmetry
reductions of the three-dimensional incompressible Navier-Stokes equations"
*Journal of Physics A: Mathematical and General***31**(1998) pp 7965-7980. - 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 241-271. - P A Clarkson and T J Priestley, "Shallow water wave systems",
*Studies in Applied Mathematics***101**(1998) pp 389-432. - E L Mansfield, G J Reid and P A Clarkson, "Nonclassical reductions of a
coupled nonlinear Schrödinger system",
*Computer Physics Communications***115**(1998) pp 460-488. - 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 66-98. - P A Clarkson, N Joshi and A Pickering, "Bäcklund transformations for
the second Painlevé hierarchy: a modified truncation approach",
*Inverse Problems***15**(1999) pp 175-187. - M J Ablowitz and P A Clarkson, "Solitons and symmetries",
*Journal of Engineering Mathematics***36**(1999) pp 1-9. - D K Ludlow, P A Clarkson and A P Bassom, "Nonclassical symmetry
reductions of the two-dimensional incompressible Navier-Stokes equations",
*Studies in Applied Mathematics***103**(1999) pp 183-240. - P A Clarkson and H N Webster, "Hierarchies of exact solutions of the
discrete third Painlevé equation",
*Chaos, Solitons & Fractals***11**(2000) pp 53-71. - 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 1-16. - D K Ludlow, P A Clarkson, and A P Bassom, "New similarity solutions of
the unsteady incompressible boundar-layer equations",
*Quarterly Journal of Mechanics and Applied Mathematics***53**(2000) pp 175-206. - 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 3751-3760. - X B Hu and P A Clarkson, "Rational solutions of an extended
Lotka-Volterra equation",
*Journal of Nonlinear Mathematical Physics***9**, Supp. 1 (2002) pp 75-86. - P A Clarkson, "Painlevé equations - nonlinear special functions",
*Journal of Computational and Applied Mathematics***153**(2003) pp 127-140. - P A Clarkson and E L Mansfield, "The second Painlevé equation, its
hierarchy and associated special polynomials",
*Nonlinearity***16**(2003) pp R1-R26. - P A Clarkson, "The third Painlevé equation and associated special
polynomials",
*Journal of Physics A: Mathematical and General***36**(2003) pp 9507--9532. - P A Clarkson, "The fourth Painlevé equation and associated special
polynomials",
*Journal of Mathematical Physics***44**(2003) pp 5350-5374. - 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 13-26. - P A Clarkson, "Remarks on the Yablonskii-Vorob'ev polynomials",
*Physics Letters***A319**(2003) pp 137-144. - P A Clarkson and G V Filipuk, "Symmetric hierarchy of the fourth
Painlevé equation",
*Proceedings of Institute of Mathematics of Minsk***12**(2004) pp 82-86. - P A Clarkson, "Special polynomials associated with rational solutions of
the fifth Painlevé equation",
*Journal of Computational and Applied Mathematics***178**(2005) pp 111-129. - 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 9751-9764. - N Bila, E L Mansfield and P A Clarkson, "Symmetry
group analysis of the shallow water and semi-geostrophic systems",
*Quarterly Journal of Mechanics and Applied Mathematics***59**(2006) pp 95-123. - 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 329-401. - P A Clarkson, N Joshi, M Mazzocco, F W Nijhoff and M Noumi,
"One hundred years of PVI, the Fuchs-Painlevé 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 293-322. - 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 299-319. - G V Filipuk and P A Clarkson,
"The symmetric fourth Painlevé hierarchy and associated special polynomials",
*Studies in Applied Mathematics***121**(2008) pp 157-188. - P A Clarkson, "Rational solutions of the Boussinesq equation",
*Analysis and Applications***6**(2008) pp 349-369. - P A Clarkson, "Vortices and polynomials",
*Studies in Applied Mathematics***123**(2009) pp 37-62. - P A Clarkson, "Rational solutions of the classical Boussinesq system",
*Nonlinear Analysis: Real World Applications***10**(2009) pp 3360-3371. - 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 semi-classical Laguerre polynomials and the fourth Painlevé equation",
*Constructive Approximation***39**(2014) 223-254. [DOI:10.1007/s00365-013-9220-4] - P A Clarkson, K Jordaan and A Kelil,
"A generalized Freud weight",
*Studies in Applied Mathematics*, accepted for publication [arXiv:1510.03772]

- S Chakravarty, M J Ablowitz and P A Clarkson, "One dimensional reductions
of self-dual Yang-Mills 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 60-71. - 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**, Springer-Verlag, Berlin (2005) pp 123-163. - 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 723-740. - P A Clarkson, "The Painlevé Equations", in
*The Princeton Companion to Applied Mathematics*[Edited by Nicholas J. Higham; Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa and Jared Tanner, associate editors], Princeton University Press, Princeton (2015) pp 163-165.

- 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**, Springer-Verlag, Berlin (1983) pp 135-142. - 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 209-210. - P A Clarkson, "New similarity reductions of Boussinesq-type 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 575-576. - 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), Springer-Verlag, Berlin-Heidelberg (1990) pp 42-45. - 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 72-79. - 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), Springer-Verlag, Berlin (1991) pp 246-254. - 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 1-31. - P A Clarkson and E L Mansfield, "Nonclassical symmetry reductions and
exact solutions of nonlinear reaction-diffusion 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 375-389. - 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 315-330. - S Hood and P A Clarkson, "Symmetry reductions of the Davey-Stewartson
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 395-404. - 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 415-430. - 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 341-352. - 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 155-171. - 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 97-101. - 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 336-339. - 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 2911-2916. - 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 63-77. - X-B Hu and P A Clarkson, "Bäcklund transformation and new explicit
solutions of the two-dimensional 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 15-22. - 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 79-89. - 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, Springer-Verlag, New York (1999) pp 591-660. - 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 139-146. - 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 129-139. - 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 195-205. - 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 113-129. - 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 47-57. - P A Clarkson, "On rational solutions of the fourth Painlevé equation and its Hamiltonian",
in
*Group Theory and Numerical Analysis*[Editors P Winternitz, D Gomez-Ullate, 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 103-118. - 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**, Springer-Verlag, Berlin (2006) pp 331-411. - P A Clarkson, "Special polynomials associated with rational and algebraic
solutions of the Painlevé equations", in
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