Publications for Professor Peter Clarkson

Journal Articles

  1. Rational solutions of the classical Boussinesq system, Peter A. Clarkson, Nonlinear Analysis: Real World Applications, 10, pages 3360-3371, 2009.
  2. Vortices and polynomials, P.A. Clarkson, Studies in Applied Mathematics, 123, pages 37-62, 2009.
  3. Rational solutions of the Boussinesq equation, Peter A. Clarkson, Analysis and Applications, 6, pages 349-369, 2008.
  4. The symmetric fourth Painlevé hierarchy and associated special polynomials, Galina V. Filipuk and Peter A. Clarkson, Studies in Applied Mathematics, 121, pages 157-188, 2008.
  5. On the Lax pairs of symmetric Painlevé equations, A. Sen, A.N.W. Hone and P.A. Clarkson, Studies in Applied Mathematics, 117, pages 299-319, 2006.
  6. Painlevé analysis and similarity reductions for the magma equations, S.E. Harris and P.A. Clarkson, Symmetry, Integrability and Geometry: Methods and Applications, 2, 068, 17 pages, 2006.
  7. Special polynomials associated with rational solutions of the defocusing nonlinear Schrodinger equation and the fourth Painlevé equation, P.A. Clarkson, European Journal of Applied Mathematics, 17, pages 293-322, 2006.
  8. Symmetry group analysis of the shallow water and semi-geostrophic systems, N. Bila, E.L. Mansfield and P.A. Clarkson, Quarterly Journal of Mechanics and Applied Mathematics, 59, pages 95-123, 2006.
  9. Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations, P.A. Clarkson, Computational Methods and Function Theory, 6, pages 329-401, 2006.
  10. Special polynomials associated with rational solutions of the fifth Painlevé equation, P.A. Clarkson, Journal of Computational and Applied Mathematics, 178, pages 111-129, 2005.
  11. Darboux transformations and the symmetric fourth Painlevé equation, A. Sen, A.N.W. Hone and P.A. Clarkson, Journal of Physics A: Mathematical and General, 38, pages 9751-9764, 2005.  
  12. The second Painlevé equation, its hierarchy and associated special polynomials, Peter A Clarkson and Elizabeth L Mansfield, Nonlinearity, 16 R(3), pages 1-26, May 2003. [External Link]  
  13. Remarks on the Yablonskii--Vorob'ev polynomials, Peter A. Clarkson, Physics Letters A, 319, pages 137-144, 2003.  
  14. Hierarchies of difference equations and Backlund transformations, Peter A. Clarkson, A.N.W. Hone and Nalini Joshi, Journal of Nonlinear Mathematical Physics, 10(Supp. 2), pages 13-26, 2003. [External Link]    
  15. The fourth Painlevé equation and associated special polynomials, Peter A. Clarkson, Journal of Mathematical Physics, 44(11), pages 5350-5374, 2003.  
  16. The third Painlevé equation and associated special polynomials, Peter A. Clarkson, Journal of Physics A: Mathematical and General, 36, pages 9507-9532, 2003.   
  17. Painlevé equations - nonlinear special functions, Peter A Clarkson, Journal of Computational and Applied Mathematics, 153(1-2), pages 127-140, 2003. [External Link]    
  18. Rational solutions of an extended Lotka-Volterra equation, Xing-Biao Hu and Peter A Clarkson, Journal of Nonlinear Mathematical Physics, 9(supp. 1), pages 75-86, 2002. [External Link]    
  19. The symmetry reductions of a turbulence model, M S Bruzon, P A Clarkson, M L Gandarias and E Medina, Journal of Physics A: Mathematical and General, 34, pages 3751-3760, 2001. [External Link]    

Conference Articles

  1. Painlevé equations - nonlinear special functions, P.A. Clarkson, In Orthogonal Polynomials and Special Functions: Computation and Application, F. Marcellan and W. van Assche (Eds.), Lecture Notes in Mathematics, volume 1883, pages 331-411, Springer-Verlag, Berlin, 2006.
  2. On rational solutions of the fourth Painlevé equation and its Hamiltonian, P.A. Clarkson, in Group Theory and Numerical Analysis, P. Winternitz et al. (Eds.), Centre de Recherches Mathématiques Proceedings and Lecture Notes Series, volume 39, pages 103-118, American Mathematical Society, Providence, RI, USA, 2005.
  3. Rational solutions of the fourth Painlevé equation and the nonlinear Schrödinger equation, P.A. Clarkson, in Group Analysis of Differential Equations, N.H. Ibragimov, C. Sophocleous and P.A. Damianou (Eds.), pages 47-57, 2005.
  4. Open problems in symmetry analysis, Peter A Clarkson and Elizabeth L Manfield, In Geometrical Study of Differential Equations, volume Contemporary Mathematics Series, volume 285, pages 195-205, Providence, RI, USA, 2001. American Mathematical Society.   
  5. On discrete Painlevé equations as Backlund transformations, Peter A Clarkson, Elizabeth L Mansfield and Helen N Webster, In Backlund and Darboux Transformations.The Geometry of Solitons, volume Centre de Recherches Mathematiques Proceedings and Lecture Notes Series, volume 29, pages 129-139, Providence, RI, USA, 2001. American Mathematical Society.   

Book Articles

  1. Painlevé equations and associated polynomials, P.A. Clarkson, in Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman, M.E.H. Ismail and E. Koelink (Eds.), Developments in Mathematics, volume 13, pages 123-163, Springer-Verlag, Berlin, 2005.