Professor Peter A Clarkson


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.

Current Teaching

  • MA593 Topics in Modern Applied Mathematics
  • MA871 Asymptotics and Perturbation Methods

    London Mathematical Society


    Research Interests


    Digital Library of Mathematical Functions Project


    SIAM Activity Group on Orthogonal Polynomials and Special Functions


    Forthcoming Conferences


    Editorial Board Membership


    Publications

    Books

    1. 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).
    2. 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).

    Edited Volumes

    1. 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).
    2. 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).
    3. 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).
    4. 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).

    Papers

    1. P A Clarkson and J B McLeod, "A note on solutions of Painlevé II", Physics Letters A92 (1982) pp 425-426.
    2. P A Clarkson, "The Painlevé property and a partial differential equation with an essential singularity", Physics Letters A109 (1985) pp 205-208.
    3. P A Clarkson, "Remarks on the two-dimensional Sine-Gordon equation and the Painlevé tests", Letters in Mathematical Physics 10 (1986) pp 297-299.
    4. P A Clarkson, "The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation", Physica D19 (1986) pp 447-450.
    5. 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.
    6. P A Clarkson, R J LeVeque and R Saxton, "Solitary wave interactions in elastic rods", Studies in Applied Mathematics 75 (1986) pp 95-121.
    7. 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.
    8. P A Clarkson, "Painlevé analysis for the damped, driven nonlinear Schrödinger equation", Proceedings of the Royal Society of Edinburgh 109A (1988) pp 109-126.
    9. 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.
    10. P A Clarkson, "New similarity solutions of the modified Boussinesq equation", Journal of Physics A: Mathematical & General 22 (1989) pp 2355-2367.
    11. 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.
    12. 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.
    13. P A Clarkson and M D Kruskal, "New similarity solutions of the Boussinesq equation", Journal of Mathematical Physics 30 (1989) pp 2201-2213.
    14. 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.
    15. 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.
    16. P A Clarkson, "New exact solutions of the Boussinesq equation", European Journal of Applied Mathematics 1 (1990) pp 279-300.
    17. 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.
    18. P A Clarkson and P Winternitz, "Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation", Physica D49 (1991) pp 257-272.
    19. 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.
    20. P A Clarkson, "Nonclassical similarity reductions and exact solutions of a generalized nonlinear Schrödinger equation", Nonlinearity 5 (1992) pp 453-472.
    21. 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.
    22. 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.
    23. P A Clarkson and S Hood, "Nonclassical symmetry reductions of the Zabalotskaya-Khoklov equation", European Journal of Applied Mathematics 3 (1992) pp 381-414.
    24. 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.
    25. 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.
    26. P A Clarkson, "Nonclassical symmetry reductions of nonlinear partial differential equations", Mathematical and Computer Modelling 18 Issue 10 (1993) pp 45-68.
    27. 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.
    28. 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.
    29. P A Clarkson and E L Mansfield, "On a shallow water wave equation", Nonlinearity 7 (1994) pp 975-1000.
    30. 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.
    31. A P Bassom and P A Clarkson, "New exact solutions of the discrete fourth Painlevé equation", Physics Letters A194 (1994) pp 358-370.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. P A Clarkson, "Nonclassical symmetry reductions for the Boussinesq equation", Chaos, Solitons & Fractals 5 (1995) pp 2261-2301.
    37. P A Clarkson and P J Olver, "Symmetry and the Chazy equation", Journal of Differential Equations 124 (1996) pp 225-246.
    38. 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.
    39. 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.
    40. 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.
    41. 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.
    42. 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.
    43. 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.
    44. 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.
    45. 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.
    46. 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.
    47. 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.
    48. 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.
    49. 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.
    50. 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.
    51. P A Clarkson and T J Priestley, "Shallow water wave systems", Studies in Applied Mathematics 101 (1998) pp 389-432.
    52. 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.
    53. 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.
    54. 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.
    55. M J Ablowitz and P A Clarkson, "Solitons and symmetries", Journal of Engineering Mathematics 36 (1999) pp 1-9.
    56. 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.
    57. 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.
    58. 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.
    59. 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.
    60. 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.
    61. 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.
    62. P A Clarkson, "Painlevé equations - nonlinear special functions", Journal of Computational and Applied Mathematics 153 (2003) pp 127-140.
    63. P A Clarkson and E L Mansfield, "The second Painlevé equation, its hierarchy and associated special polynomials", Nonlinearity 16 (2003) pp R1-R26.
    64. P A Clarkson, "The third Painlevé equation and associated special polynomials", Journal of Physics A: Mathematical and General 36 (2003) pp 9507--9532.
    65. P A Clarkson, "The fourth Painlevé equation and associated special polynomials", Journal of Mathematical Physics 44 (2003) pp 5350-5374.
    66. 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.
    67. P A Clarkson, "Remarks on the Yablonskii-Vorob'ev polynomials", Physics Letters A319 (2003) pp 137-144.
    68. 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.
    69. 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.
    70. 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.
    71. 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.
    72. 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.
    73. 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.
    74. 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.
    75. 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).
    76. 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.
    77. 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.
    78. P A Clarkson, "Rational solutions of the Boussinesq equation", Analysis and Applications 6 (2008) pp 349-369.
    79. P A Clarkson, "Vortices and polynomials", Studies in Applied Mathematics 123 (2009) pp 37-62.
    80. P A Clarkson, "Rational solutions of the classical Boussinesq system", Nonlinear Analysis: Real World Applications 10 (2009) pp 3360-3371.
    81. 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).
    82. 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).
    83. 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]

    Chapters in Books

    1. 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.
    2. 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.
    3. 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.

    Papers in Conference Proceedings

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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).
    17. 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).
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. 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 Loday-Richaud], Séminaires et Congrès, vol. 14, Sociètè Mathèmatique de France, Paris (2007) pp 21-52.
    31. 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 Loday-Richaud], Séminaires et Congrès, vol. 14, Sociètè Mathèmatique de France, Paris (2007) pp 53-64.
    32. 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 69-84.
    33. 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 62-76.


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