School of Mathematics, Statistics & Actuarial Science

About

Peter chairs the School's Athena SWAN Committee and is a member of the University's Athena SWAN working group. In addition to his work at the University of Kent, Peter is a member of the London Mathematical Society's Women in Mathematics Committee and Chair of the steering committee for the LMS Good Practice Scheme. The Good Practice Scheme 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.

NIST Digital Library of Mathematical Functions project: Peter is a 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. Peter's role in the project is with writing the chapter on Painlevé Transcendents.

Contact Information

Address

Room 128

Office hours: Please email me to make an appointment

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Publications

A number of Peter's publications not listed below are itemised on his personal web page

Also view these in the Kent Academic Repository

Article
Rogers, C. and Clarkson, P. (2017). Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System. Symmetry, Integrability and Geometry: Methods and Applications [Online] 13. Available at: https://doi.org/10.3842/SIGMA.2017.018.
Ankiewicz, A. et al. (2017). Conservation Laws and Integral Relations for the Boussinesq Equation. Studies in Applied Mathematics [Online]. Available at: https://dx.doi.org/10.1111/sapm.12174.
Clarkson, P., Loureiro, A. and Van Assche, W. (2016). Unique positive solution for an alternative discrete Painlevé I equation. Journal of Difference Equations and Applications [Online]. Available at: http://www.tandfonline.com/doi/abs/10.1080/10236198.2015.1127917.
Clarkson, P. (2016). On Airy Solutions of the Second Painleve Equation. Studies in Applied Mathematics [Online] 137:93-109. Available at: http://dx.doi.org/10.1111/sapm.12123.
Clarkson, P., Jordaan, K. and Kelil, A. (2015). A Generalized Freud Weight. Studies in Applied Mathematics [Online] 136:288-320. Available at: http://dx.doi.org/10.1111/sapm.12105.
Clarkson, P. and Jordaan, K. (2014). The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation. Constructive Approximation [Online] 39:223-254. Available at: http://dx.doi.org/10.1007/s00365-013-9220-4.
Clarkson, P. and Jordaan, K. (2014). The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation. Constructive Approximation [Online] 39:223-254. Available at: http://link.springer.com/article/10.1007/s00365-013-9220-4.
Clarkson, P. (2013). Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Journal of Physics A: Mathematical and Theoretical [Online] 46. Available at: http://dx.doi.org/10.1088/1751-8113/46/18/185205.
Ankiewicz, A., Clarkson, P. and Akhmediev, N. (2010). Rogue waves, rational solutions, the patterns of their zeros and integral relations. Journal of Physics A: Mathematical and Theoretical [Online] 43:122002. Available at: http://dx.doi.org/10.1088/1751-8113/43/12/122002.
Clarkson, P. (2009). Vortices and Polynomials. Studies in Applied Mathematics [Online] 123:37-62. Available at: http://dx.doi.org/10.1111/j.1467-9590.2009.00446.x.
Clarkson, P. (2009). Rational solutions of the classical Boussinesq system. Nonlinear Analysis: Real World Applications [Online] 10:3360-3371. Available at: http://dx.doi.org/10.1016/j.nonrwa.2008.09.019.
Clarkson, P. (2008). Rational Solutions Of The Boussinesq Equation. Analysis and Applications [Online] 6:349-369. Available at: http://dx.doi.org/10.1142/S0219530508001250.
Clarkson, P. and Filipuk, G. (2008). The symmetric fourth Painleve hierarchy and associated special polynomials. Studies in Applied Mathematics [Online] 121:157-188. Available at: http://dx.doi.org/10.1111/j.1467-9590.2008.00410.x.
Bila, N., Mansfield, E. and Clarkson, P. (2006). Symmetry group analysis of the shallow water and semi-geostrophic equations. Quarterly Journal of Mechanics and Applied Mathematics [Online] 59:95-123. Available at: http://dx.doi.org/10.1093/qjmam/hbi033 .
Clarkson, P. (2006). Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations. Computational Methods and Function Theory 6:329-401.
Clarkson, P. (2006). Special polynomials associated with rational solutions of the defocusing nonlinear Schrodinger equation and the fourth Painleve equation. European Journal of Applied Mathematics [Online] 17:293-322. Available at: http://dx.doi.org/10.1017/S0956792506006565.
Sen, A., Hone, A. and Clarkson, P. (2006). On the Lax pairs of symmetric Painleve equations. Studies in Applied Mathematics [Online] 117:299-319. Available at: http://dx.doi.org/10.1111/j.1467-9590.2006.00356.x.
Harris, S. and Clarkson, P. (2006). Painlevé Analysis and Similarity Reductions for the Magma Equation. Symmetry, Integrability and Geometry: Methods and Applications [Online] 2. Available at: http://dx.doi.org/doi:10.3842/SIGMA.2006.068.
Clarkson, P. et al. (2006). One hundred years of PVI, the Fuchs–Painlevé equation - Preface. Journal of Physics A: Mathematical and General [Online] 39. Available at: http://dx.doi.org/10.1088/0305-4470/39/39/E01.
Sen, A., Hone, A. and Clarkson, P. (2005). Darboux transformations and the symmetric fourth Painlevé equation. Journal of Physics A: Mathematical and General [Online] 38:9751-9764. Available at: http://dx.doi.org/10.1088/0305-4470/38/45/003.
Clarkson, P. (2005). Special polynomials associated with rational solutions of the fifth Painlevé equation. Journal of Computational and Applied Mathematics [Online] 178:111-129. Available at: http://dx.doi.org/10.1016/j.cam.2004.04.015.
Clarkson, P. (2003). The third Painlevé equation and associated special polynomials. Journal of Physics A: Mathematical and General [Online] 36:9507-9532. Available at: http://dx.doi.org/10.1088/0305-4470/36/36/306 .
Clarkson, P. (2003). Remarks on the Yablonskii–Vorob'ev polynomials. Physics Letters A [Online] 319:137-144. Available at: http://dx.doi.org/10.1016/j.physleta.2003.10.016 .
Clarkson, P. and Mansfield, E. (2003). The second Painleve equation, its hierarchy and associated special polynomials . Nonlinearity [Online] 16:R1-R26. Available at: http://dx.doi.org/10.1088/0951-7715/16/3/201.
Clarkson, P. (2003). The fourth Painlevé equation and associated special polynomials. Journal of Mathematical Physics [Online] 44:5350-5374. Available at: http://dx.doi.org/10.1063/1.1603958 .
Clarkson, P., Hone, A. and Joshi, N. (2003). Hierarchies of Difference Equations and Bäcklund Transformations. Journal of Nonlinear Mathematical Physics [Online] 10:13-26. Available at: http://dx.doi.org/10.2991/jnmp.2003.10.s2.2.
Clarkson, P. (2003). Painlevé equations—nonlinear special functions. Journal of Computational and Applied Mathematics [Online] 153:127-140. Available at: http://dx.doi.org/10.1016/S0377-0427(02)00589-7 .
Hu, X. and Clarkson, P. (2002). Rational Solutions of an Extended Lotka-Volterra Equation. Journal of Nonlinear Mathematical Physics [Online] 9:75-93. Available at: http://dx.doi.org/10.2991/jnmp.2002.9.s1.7 .
Bruzón, M. et al. (2001). The symmetry reductions of a turbulence model. Journal of Physics A: Mathematical and General [Online] 34:3751-3760. Available at: http://dx.doi.org/10.1088/0305-4470/34/18/304.
Ludlow, D., Clarkson, P. and Bassom, A. (2000). New similarity solutions of the unsteady incompressible boundary-layer equations. Quarterly Journal of Mechanics and Applied Mathematics [Online] 53:175-206. Available at: http://dx.doi.org/10.1093/qjmam/53.2.175 .
Ludlow, D., Clarkson, P. and Bassom, A. (1999). Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations. Studies in Applied Mathematics [Online] 103:183-240. Available at: http://dx.doi.org/10.1111/1467-9590.00125.
Ablowitz, M. and Clarkson, P. (1999). Solitons and symmetries. Journal of Engineering Mathematics [Online] 36:1-9. Available at: http://dx.doi.org/10.1023/A:1004581620608.
Clarkson, P., Joshi, N. and Pickering, A. (1999). Backlund transformations for the second Painleve hierarchy: a modified truncation approach. Inverse Problems [Online] 15:175-187. Available at: http://dx.doi.org/10.1088/0266-5611/15/1/019.
Clarkson, P. and Priestley, T. (1999). Symmetries of a class of nonlinear fourth order partial differential equations. Journal of Nonlinear Mathematical Physics [Online] 6:66-98. Available at: http://dx.doi.org/10.2991/jnmp.1999.6.1.6 .
Mansfield, E., Reid, G. and Clarkson, P. (1998). Nonclassical reductions of a 3+1-cubic nonlinear Schrodinger system. Computer Physics Communications [Online] 115:460-488. Available at: http://dx.doi.org/10.1016/S0010-4655(98)00136-2.
Ludlow, D., Clarkson, P. and Bassom, A. (1998). Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Journal of Physics A: Mathematical and General [Online] 31:7965-7980. Available at: http://dx.doi.org/10.1088/0305-4470/31/39/012.
Clarkson, P. and Priestley, T. (1998). Shallow water wave systems. Studies in Applied Mathematics [Online] 101:389-432. Available at: http://dx.doi.org/10.1111/1467-9590.00099.
Bassom, A. et al. (1998). Application of uniform asymptotics to the second painleve transcendent. Archive for Rational Mechanics and Analysis [Online] 143:241-71. Available at: http://dx.doi.org/10.1007/s002050050105.
Hu, X. and Clarkson, P. (1998). Backlund transformations and nonlinear superposition formulae of a differential-difference KdV equation. Journal of Physics A: Mathematical and General [Online] 31:1405-1414. Available at: http://dx.doi.org/10.1088/0305-4470/31/5/010 .
Hu, X., Clarkson, P. and Bullough, R. (1997). New integrable differential-difference systems. Journal of Physics A: Mathematical and General 30:L669-L676.
Milne, A., Clarkson, P. and Bassom, A. (1997). Backlund transformations and solution hierarchies for the third Painleve equation. Studies in Applied Mathematics [Online] 98:139-194. Available at: http://dx.doi.org/10.1111/1467-9590.00044.
Mansfield, E. and Clarkson, P. (1997). Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations. Journal of Symbolic Computation [Online] 23:517-533. Available at: http://dx.doi.org/10.1006/jsco.1996.0105 .
Milne, A., Clarkson, P. and Bassom, A. (1997). Application of the isomonodromy deformation method to the fourth Painleve equation. Inverse Problems [Online] 13:421-439. Available at: http://dx.doi.org/10.1088/0266-5611/13/2/015 .
Clarkson, P., Mansfield, E. and Priestley, T. (1997). Symmetries of a class of nonlinear third-order partial differential equations. Mathematical and Computer Modelling 25:195-212.
Clarkson, P., Gordoa, P. and Pickering, A. (1997). Multicomponent equations associated to non-isospectral scattering problems. Inverse Problems [Online] 13:1463-1476. Available at: http://dx.doi.org/10.1088/0266-5611/13/6/004.
Mansfield, E. and Clarkson, P. (1997). Symmetries and exact solutions for a 2+1-dimensional shallow water wave equation. Mathematics and Computers in Simulation [Online] 43:39-55. Available at: http://dx.doi.org/10.1016/S0378-4754(96)00054-7 .
Clarkson, P. and Olver, P. (1996). Symmetry and the Chazy equation. Journal of Differential Equations [Online] 124:225-246. Available at: http://dx.doi.org/10.1006/jdeq.1996.0008.
Clarkson, P., Mansfield, E. and Milne, A. (1996). Symmetries and exact solutions of a 2+1 dimensional sine-Gordon equation. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences. 354:1807-1835.
Clarkson, P., Mansfield, E. and Milne, A. (1996). Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences. [Online] 354:1807-1835. Available at: http://dx.doi.org/10.1098/rsta.1996.0079.
Hu, X. and Clarkson, P. (1995). Rational Solutions of a Differential -Difference KDV Equation, the Equation and Equation and the discret Equetion . Journal of Physics A: Mathematical and General [Online] 28:5009-5016. Available at: http://dx.doi.org/10.1088/0305-4470/28/17/029.
Bassom, A., Clarkson, P. and Hicks, A. (1995). Backlund-Transformations and Solution Hierarchies for the 4th Painleve Equation . Studies in Applied Mathematics 95:1-71.
Book section
Clarkson, P. (2008). The fourth Painleve equation. in: Guo, L. and Sit, W. Y. eds. Differential Algebra and Related Topics. Singapore: World Scientific. Available at: http://www.worldscibooks.com/mathematics/6969.html.
Clarkson, P., Joshi, N. and Mazzocco, M. (2006). The Lax pair for the mKdV hierarchy. in: Delabaere, E. and Loday-Richaud, M. eds. Théories Asymptotiques et Equations de Painlevé. Paris, France: Sociètè Mathèematique de France, pp. 53-64.
Clarkson, P. (2006). Special polynomials associated with rational and algebraic solutions of the Painleve equations. in: Delabaere, E. and Loday-Richaud, M. eds. Theories Asymptotiques et Equations de Painleve. Paris, France: Societe Mathematique de France, pp. 21-52.
Clarkson, P. (2006). Painleve equations - nonlinear special functions. in: Marcellan, F. and van Asschel, W. eds. Orthogonal Polynomials and Special Functions: Computation and Application. Berlin/ Heidelberg: Springer-Verlag, pp. 331-411. Available at: http://dx.doi.org/10.1007/978-3-540-36716-1_7.
Clarkson, P. (2005). Painlevé Equations and Associated Polynomials. in: Ismail, M. E. H. and Koelink, E. eds. Theory and Applications of Special Functions: A Volume Dedicated to Mizan Rahman. Berlin: Springer, pp. 123-163. Available at: http://dx.doi.org/10.1007/0-387-24233-3_7.
Clarkson, P. (2003). On rational solutions of the fourth Painleve equation and its Hamiltonian. in: Winternitz, P. et al. eds. Group Theory and Numerical Analysis . United States: American Mathematical Society, pp. 103-118.
Clarkson, P. and Cosgrove, C. (2002). Symmetry, the Chazy equation and Chazy hierarchies. in: Harnad, J. and Its, A. eds. Isomondromic Deformations and Applications in Physics. United States: American Mathematical Society, pp. 113-129.
Clarkson, P. and Mansfield, E. (2002). Open problems in symmetry analysis. in: Leslie, J. ed. The Geometrical Study of Differential Equations. United Kingdom: American Mathematical Society, pp. 195-205.
Clarkson, P., Mansfield, E. and Webster, H. (2002). On Discrete Painleve Equations as Backlund Transformations. in: Coley, A. et al. eds. Backlund and Darboux Transformations: The Geometry of Solitons . United States: American Mathematical Society, pp. 129-139.
Monograph
Rogers, C. and Clarkson, P. (2017). Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System. arXiv.org. Available at: https://arxiv.org/abs/1701.03238.
Clarkson, P., Law, C. and Lin, C. (2016). An algebraic proof for the Umemura polynomials for the third Painlevé equation. arxiv.org. Available at: https://arxiv.org/abs/1609.00495.
Clarkson, P. and Dowie, E. (2016). Rational solutions of the Boussinesq equation and applications to rogue waves. arxiv.org. Available at: https://arxiv.org/abs/1609.00503.
Ankiewicz, A. et al. (2016). Conservation laws and integral relations for the Boussinesq equation. arXiv.org. Available at: https://arxiv.org/abs/1611.09505.
Clarkson, P. and Jordaan, K. (2016). Properties of Generalized Freud Polynomials. arxiv.org. Available at: https://arxiv.org/abs/1606.06026.
Conference or workshop item
Clarkson, P. (2008). Asymptotics of the second Painleve equation. in: Dominici, D. and Maier, R. eds. Providence, RI, USA: American Mathematical Society, pp. 69-83.
Clarkson, P., Mansfield, E. and Webster, H. (2000). On the relation between the continuous and discrete Painleve equations. in: 12th International Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS 98). Springer Science and Business Media, pp. 1-16. Available at: http:di.dox.org/10.1007/BF02551165.
Clarkson, P. and Webster, H. (2000). Hierarchies of exact solutions for the discrete third Painleve equation. in: Dg Iii, B. G. I., Poles, V. U. B. T. P. D. T. and Cultural, A. eds. 2nd Brussels Meeting on Integrability and Chaos in Discrete Systems. Pergamon-Elsevier Science Ltd, pp. 53-71. Available at: http://dx.doi.org/10.1016/S0960-0779(98)00268-9.
Total publications in KAR: 68 [See all in KAR]
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Research Interests

  • 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. equations.
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Teaching

MA617/MA871: Asymptotics and Perturbation Methods
MA6544/MA7544: Nonlinear Systems and Applications back to top

Research Supervisees

  • Ellen Dowie - nonlinear partial differential equations and soliton theory
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School of Mathematics, Statistics and Actuarial Science (SMSAS), Sibson Building, Parkwood Road, Canterbury, CT2 7FS

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Last Updated: 06/07/2017