## Clarkson, Peter A.

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 Author ID: clarkson.peter-a Published as: Clarkson, Peter A.; Clarkson, P. A.; Clarkson, Peter; Klarkson, P. A. more...less Homepage: https://www.kent.ac.uk/mathematics-statistics-actuarial-science/people/404/www.k... External Links: MGP · ORCID · Google Scholar · Math-Net.Ru · dblp
 Documents Indexed: 119 Publications since 1982, including 1 Book 4 Contributions as Editor Co-Authors: 53 Co-Authors with 89 Joint Publications 1,337 Co-Co-Authors
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### Co-Authors

 32 single-authored 15 Bassom, Andrew P. 15 Mansfield, Elizabeth Louise 6 Ablowitz, Mark Jay 6 Ludlow, David K. 6 McLeod, John Bryce 5 Hicks, Andrew C. 4 Hood, Simon 4 Hu, Xingbiao 4 Jordaan, Kerstin 4 Joshi, Nalini 4 Milne, Alice E. 4 Priestley, Thomas J. 3 Hone, Andrew N. W. 3 Rogers, Colin 3 Webster, Helen N. 2 Ankiewicz, Adrian 2 Cosgrove, Christopher M. 2 Dowie, Ellen 2 Kruskal, Martin David 2 Mazzocco, Marta 2 Nijhoff, Frank W. 2 Olver, Peter John 2 Pickering, Andrew 2 Winternitz, Pavel 1 Akhmediev, Nail N. 1 Bîlă, Nicoleta Virginia 1 Bruzón, Maria Santos 1 Bullough, Robin K. 1 Chiu, Tin Lok 1 Chow, Kwok Wing 1 Filipuk, Galina V. 1 Fokas, Athanassios S. 1 Gandarias Núñez, Maria Luz 1 Gómez-Ullate, David 1 Gordoa, Pilar Ruiz 1 Grandati, Yves 1 Harris, Shirley Elizabeth 1 Hu, Xingbao 1 Kelil, Abey Sherif 1 Law, Chun-Kong 1 LeVeque, Randall J. 1 Liu, Tianyang 1 Loureiro, Ana Filipa 1 Milson, Robert 1 Noumi, Masatoshi 1 Olde Daalhuis, Adri B. 1 Qian, Xianmin 1 Ramani, Alfred 1 Reid, Gregory John 1 Saxton, Ralph A. 1 Thomas, Bryn 1 Tuszynski, Jack A. 1 Van Assche, Walter
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### Serials

 14 Studies in Applied Mathematics 13 Journal of Physics A: Mathematical and General 4 Journal of Nonlinear Mathematical Physics 3 Inverse Problems 3 Journal of Mathematical Physics 3 Nonlinearity 3 Chaos, Solitons and Fractals 3 Physica D 3 European Journal of Applied Mathematics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Archive for Rational Mechanics and Analysis 2 IMA Journal of Applied Mathematics 2 Journal of Engineering Mathematics 2 Journal of Mathematical Analysis and Applications 2 Physics Letters. A 2 Quarterly Journal of Mechanics and Applied Mathematics 2 Journal of Computational and Applied Mathematics 2 Mathematical and Computer Modelling 2 SIAM Journal on Applied Mathematics 2 London Mathematical Society Lecture Note Series 2 Journal of Physics A: Mathematical and Theoretical 1 Computer Physics Communications 1 Letters in Mathematical Physics 1 Theoretical and Mathematical Physics 1 Journal of Approximation Theory 1 Journal of Differential Equations 1 Mathematics and Computers in Simulation 1 Acta Applicandae Mathematicae 1 Constructive Approximation 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Mathematical Analysis 1 Methods and Applications of Analysis 1 Advances in Differential Equations 1 Integral Transforms and Special Functions 1 Journal of Difference Equations and Applications 1 Chaos 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Physical Review Letters 1 Nonlinear Analysis. Real World Applications 1 Computational Methods and Function Theory 1 Analysis and Applications (Singapore) 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 African Journal of Mathematical Physics 1 Transactions of Mathematics and its Applications
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### Fields

 72 Partial differential equations (35-XX) 52 Ordinary differential equations (34-XX) 35 Dynamical systems and ergodic theory (37-XX) 30 Special functions (33-XX) 23 Global analysis, analysis on manifolds (58-XX) 15 Fluid mechanics (76-XX) 11 Difference and functional equations (39-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 3 Computer science (68-XX) 2 Topological groups, Lie groups (22-XX) 2 Numerical analysis (65-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

108 Publications have been cited 3,632 times in 2,911 Documents Cited by Year
Solitons, nonlinear evolution equations and inverse scattering. Zbl 0762.35001
Ablowitz, M. J.; Clarkson, P. A.
1991
New similarity reductions of the Boussinesq equation. Zbl 0698.35137
Clarkson, Peter A.; Kruskal, Martin D.
1989
Symmetry reductions and exact solutions of a class of nonlinear heat equations. Zbl 0812.35017
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
Solitary-wave interactions in elastic rods. Zbl 0606.73028
Clarkson, Peter A.; LeVeque, Randall J.; Saxton, Ralph
1986
Painlevé analysis of the nonlinear Schrödinger family of equations. Zbl 0632.35073
Clarkson, Peter A.; Cosgrove, Christopher M.
1987
Algorithms for the nonclassical method of symmetric reductions. Zbl 0823.58036
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
1996
On a shallow water wave equation. Zbl 0803.35111
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach. Zbl 0923.35170
Clarkson, Peter A.; Joshi, Nalini; Pickering, Andrew
1999
Painlevé equations – nonlinear special functions. Zbl 1100.33006
Clarkson, Peter A.
2006
Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation. Zbl 0868.35132
Hu, Xing-Biao; Clarkson, Peter A.
1995
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
1995
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
2003
Exact solutions of the multidimensional derivative nonlinear Schrödinger equation for many-body systems near criticality. Zbl 0738.35090
Clarkson, Peter A.; Tuszyński, J. A.
1990
New similarity reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations. Zbl 0711.35113
Clarkson, Peter A.
1989
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Zbl 0734.35123
Clarkson, P. A.; Winternitz, P.
1991
The Painlevé-Kowalevski and poly-Painlevé tests for integrability. Zbl 0803.35128
Kruskal, Martin D.; Clarkson, Peter A.
1992
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
1990
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
1989
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
1990
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
2003
Vortices and polynomials. Zbl 1372.37110
Clarkson, P. A.
2009
Rational solutions of the Boussinesq equation and applications to rogue waves. Zbl 1403.37073
Clarkson, Peter A.; Dowie, Ellen
2017
Multicomponent equations associated to non-isospectral scattering problems. Zbl 0889.35094
Clarkson, Peter A.; Gordoa, Pilar R.; Pickering, Andrew
1997
Rogue waves, rational solutions, the patterns of their zeros and integral relations. Zbl 1189.35300
Ankiewicz, Adrian; Clarkson, Peter A.; Akhmediev, Nail
2010
Hodograph transformations of linearizable partial differential equations. Zbl 0694.35005
Clarkson, P. A.; Fokas, A. S.; Ablowitz, M. J.
1989
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
1990
Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations. Zbl 0788.35067
Clarkson, P. A.; Mansfield, E. L.
1993
The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation. Zbl 1321.34115
Clarkson, Peter A.; Jordaan, Kerstin
2014
The fourth Painlevé equation and associated special polynomials. Zbl 1063.33029
Clarkson, Peter A.
2003
Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation. Zbl 0752.35064
Clarkson, Peter A.
1992
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Zbl 0846.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
1995
Symmetries and exact solutions of a $$(2+1)$$-dimensional sine-Gordon system. Zbl 0862.35104
Clarkson, Peter A.; Mansfield, Elizabeth L.; Milne, Alice E.
1996
Application of uniform asymptotics to the second Painlevé transcendent. Zbl 0912.34007
Bassom, Andrew P.; Clarkson, Peter A.; Law, C. K.; McLeod, J. Bryce
1998
Bäcklund transformations and solution hierarchies for the third Painlevé equation. Zbl 0878.34006
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
Symmetries of a class of nonlinear third-order partial differential equations. Zbl 0879.35005
Clarkson, P. A.; Mansfield, E. L.; Priestley, T. J.
1997
Symmetry reductions and exact solutions of shallow water wave equations. Zbl 0835.35006
Clarkson, Peter A.; Mansfield, Elizabeth L.
1995
A connection formula for the second Painlevé transcendent. Zbl 0653.34020
Clarkson, Peter A.; McLeod, J. Bryce
1988
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 0952.37019
Clarkson, Peter A.
1995
Remarks on the Yablonskii-Vorob’ev polynomials. Zbl 1053.34082
Clarkson, Peter A.
2003
Integral equations and exact solutions for the fourth Painlevé equation. Zbl 0751.34002
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.; McLeod, J. B.
1992
Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations. Zbl 1112.33015
Clarkson, Peter A.
2006
A generalized Freud weight. Zbl 1336.33022
Clarkson, Peter A.; Jordaan, Kerstin; Kelil, Abey
2016
Painlevé analysis of the damped, driven nonlinear Schrödinger equation. Zbl 0681.35077
Clarkson, Peter A.
1988
Properties of generalized Freud polynomials. Zbl 1437.33011
Clarkson, Peter A.; Jordaan, Kerstin
2018
Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations. Zbl 1136.76342
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
1999
Nonclassical symmetry reductions of nonlinear partial differential equations. Zbl 0805.35092
Clarkson, P. A.
1993
The thrid Painlevé equation and associated special polynomials. Zbl 1046.33015
Clarkson, Peter A.
2003
Symmetry group analysis of the shallow water and semi-geostrophic equations. Zbl 1088.76059
Bîlă, Nicoleta; Mansfield, Elizabeth L.; Clarkson, Peter A.
2006
New similarity solutions of the unsteady incompressible boundary-layer equations. Zbl 1003.76019
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
2000
New symmetry reductions and exact solutions of the Davey-Stewartson system. I: Reductions to ordinary differential equations. Zbl 0802.76009
Clarkson, Peter A.; Hood, Simon
1994
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
1994
Special polynomials associated with rational solutions of the fifth Painlevé equation. Zbl 1077.33035
Clarkson, Peter A.
2005
On Airy solutions of the second Painlevé equation. Zbl 1346.35179
Clarkson, Peter A.
2016
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
1999
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya- Khokhlov equation. Zbl 0771.35053
Clarkson, Peter A.; Hood, Simon
1992
Numerical studies of the fourth Painlevé equation. Zbl 0782.65099
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.
1993
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
2006
Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation. Zbl 1126.35062
Clarkson, Peter A.
2006
Integrability of Klein-Gordon equations. Zbl 0629.35104
Clarkson, Peter A.; McLeod, J. Bryce; Olver, Peter J.; Ramani, Alfred
1986
New integrable differential-difference systems. Zbl 0924.35157
Hu, Xing-Biao; Clarkson, Peter A.; Bullough, Robin
1997
The symmetric fourth Painlevé hierarchy and associated special polynomials. Zbl 1202.34155
Filipuk, Galina V.; Clarkson, Peter A.
2008
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Zbl 1275.34109
Clarkson, Peter A.
2013
Nonclassical reductions of a $$(3+1)$$-cubic nonlinear Schrödinger system. Zbl 0996.35069
Mansfield, Elizabeth L.; Reid, Gregory J.; Clarkson, Peter A.
1998
Open problems in symmetry analysis. Zbl 1172.35306
Clarkson, Peter A.; Mansfield, Elizabeth L.
2001
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
2016
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation. Zbl 0616.35080
Clarkson, Peter A.
1986
On rational solutions of the fourth Painlevé equation and its Hamiltonian. Zbl 1091.34052
Clarkson, P. A.
2005
Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Zbl 0931.35125
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
1998
Symmetries and exact solutions for a $$2+1$$-dimensional shallow water wave equation. Zbl 0869.68060
Mansfield, Elizabeth L.; Clarkson, Peter A.
1997
Symmetry reductions of a generalized, cylindrical nonlinear Schrödinger equation. Zbl 0772.35065
Clarkson, Peter A.; Hood, Simon
1993
The symmetry reductions of a turbulence model. Zbl 1002.35009
Bruzón, M. S.; Clarkson, P. A.; Gandarias, M. L.; Medina, E.
2001
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
2006
Darboux transformations and the symmetric fourth Painlevé equation. Zbl 1102.34071
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
2005
Hierarchies of difference equations and Bäcklund transformations. Zbl 1362.39006
Clarkson, Peter A.; Hone, Andrew N. W.; Joshi, Nalini
2003
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
2017
Integral equations and connection formulae for the Painlevé equations. Zbl 0856.34009
Clarkson, P. A.; McLeod, J. B.
1992
The classical, direct, and nonclassical methods for symmetry reductions of nonlinear partial differential equations. Zbl 0901.58069
Clarkson, Peter A.; Ludlow, David K.; Priestley, Thomas J.
1997
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
1999
Asymptotics of the second Painlevé equation. Zbl 1185.33027
Clarkson, Peter A.
2008
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
1999
Ermakov-Painlevé II reduction in cold plasma physics. Application of a Bäcklund transformation. Zbl 1411.37061
Rogers, Colin; Clarkson, Peter A.
2018
On integrable Ermakov-Painlevé IV systems. Zbl 1393.34083
Rogers, Colin; Bassom, Andrew P.; Clarkson, Peter A.
2018
Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests. Zbl 0591.35061
Clarkson, Peter A.
1985
New exact solutions of the discrete fourth Painlevé equation. Zbl 0941.39502
Bassom, Andrew P.; Clarkson, Peter A.
1994
Application of the isomonodromy deformation method to the fourth Painlevé equation. Zbl 0872.35108
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
Rational solutions and Bäcklund transformations for the third Painlevé equation. Zbl 0794.34001
Milne, A. E.; Clarkson, P. A.
1993
Symmetry reductions and exact solutions for a generalised Boussinesq equation. Zbl 0793.35076
Ludlow, D. K.; Clarkson, P. A.
1993
On the Lax pairs of the symmetric Painlevé equations. Zbl 1145.34380
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
2006
Special polynomials associated with rational and algebraic solutions of the Painlevé equations. Zbl 1165.34057
Clarkson, Peter A.
2006
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
2017
Rational solutions of an extended Lotka-Volterra equation. Zbl 1362.34099
Hu, X. B.; Clarkson, P. A.
2002
Open problems for Painlevé equations. Zbl 1416.33028
Clarkson, Peter A.
2019
Rational solutions of the classical Boussinesq system. Zbl 1179.35282
Clarkson, Peter A.
2009
On the application of solutions of the fourth Painlevé equation to various physically motivated nonlinear partial differential equations. Zbl 0845.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
1996
Symmetry reductions and exact solutions of the Davey-Stewartson system. Zbl 0793.35100
Hood, S.; Clarkson, P. A.
1993
Rational solutions of the Boussinesq equation. Zbl 1173.33315
Clarkson, Peter A.
2008
Hierarchies of exact solutions for the discrete third Painlevé equation. Zbl 1115.34302
Clarkson, Peter A.; Webster, Helen N.
2000
Shallow water wave systems. Zbl 1020.35083
Clarkson, Peter A.; Priestley, Thomas J.
1998
A generalized sextic Freud weight. Zbl 1483.33005
Clarkson, Peter A.; Jordaan, Kerstin
2021
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
2020
Open problems for Painlevé equations. Zbl 1416.33028
Clarkson, Peter A.
2019
Properties of generalized Freud polynomials. Zbl 1437.33011
Clarkson, Peter A.; Jordaan, Kerstin
2018
Ermakov-Painlevé II reduction in cold plasma physics. Application of a Bäcklund transformation. Zbl 1411.37061
Rogers, Colin; Clarkson, Peter A.
2018
On integrable Ermakov-Painlevé IV systems. Zbl 1393.34083
Rogers, Colin; Bassom, Andrew P.; Clarkson, Peter A.
2018
Rational solutions of the Boussinesq equation and applications to rogue waves. Zbl 1403.37073
Clarkson, Peter A.; Dowie, Ellen
2017
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
2017
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
2017
A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane. Zbl 1390.35334
Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.
2017
A generalized Freud weight. Zbl 1336.33022
Clarkson, Peter A.; Jordaan, Kerstin; Kelil, Abey
2016
On Airy solutions of the second Painlevé equation. Zbl 1346.35179
Clarkson, Peter A.
2016
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
2016
The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation. Zbl 1321.34115
Clarkson, Peter A.; Jordaan, Kerstin
2014
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Zbl 1275.34109
Clarkson, Peter A.
2013
Rogue waves, rational solutions, the patterns of their zeros and integral relations. Zbl 1189.35300
Ankiewicz, Adrian; Clarkson, Peter A.; Akhmediev, Nail
2010
Vortices and polynomials. Zbl 1372.37110
Clarkson, P. A.
2009
Rational solutions of the classical Boussinesq system. Zbl 1179.35282
Clarkson, Peter A.
2009
The symmetric fourth Painlevé hierarchy and associated special polynomials. Zbl 1202.34155
Filipuk, Galina V.; Clarkson, Peter A.
2008
Asymptotics of the second Painlevé equation. Zbl 1185.33027
Clarkson, Peter A.
2008
Rational solutions of the Boussinesq equation. Zbl 1173.33315
Clarkson, Peter A.
2008
Painlevé equations – nonlinear special functions. Zbl 1100.33006
Clarkson, Peter A.
2006
Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations. Zbl 1112.33015
Clarkson, Peter A.
2006
Symmetry group analysis of the shallow water and semi-geostrophic equations. Zbl 1088.76059
Bîlă, Nicoleta; Mansfield, Elizabeth L.; Clarkson, Peter A.
2006
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
2006
Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation. Zbl 1126.35062
Clarkson, Peter A.
2006
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
2006
On the Lax pairs of the symmetric Painlevé equations. Zbl 1145.34380
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
2006
Special polynomials associated with rational and algebraic solutions of the Painlevé equations. Zbl 1165.34057
Clarkson, Peter A.
2006
Special polynomials associated with rational solutions of the fifth Painlevé equation. Zbl 1077.33035
Clarkson, Peter A.
2005
On rational solutions of the fourth Painlevé equation and its Hamiltonian. Zbl 1091.34052
Clarkson, P. A.
2005
Darboux transformations and the symmetric fourth Painlevé equation. Zbl 1102.34071
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
2005
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
2003
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
2003
The fourth Painlevé equation and associated special polynomials. Zbl 1063.33029
Clarkson, Peter A.
2003
Remarks on the Yablonskii-Vorob’ev polynomials. Zbl 1053.34082
Clarkson, Peter A.
2003
The thrid Painlevé equation and associated special polynomials. Zbl 1046.33015
Clarkson, Peter A.
2003
Hierarchies of difference equations and Bäcklund transformations. Zbl 1362.39006
Clarkson, Peter A.; Hone, Andrew N. W.; Joshi, Nalini
2003
Rational solutions of an extended Lotka-Volterra equation. Zbl 1362.34099
Hu, X. B.; Clarkson, P. A.
2002
Symmetry, the Chazy equation and Chazy hierarchies. Zbl 1011.34078
Clarkson, Peter A.; Cosgrove, Christopher M.
2002
Open problems in symmetry analysis. Zbl 1172.35306
Clarkson, Peter A.; Mansfield, Elizabeth L.
2001
The symmetry reductions of a turbulence model. Zbl 1002.35009
Bruzón, M. S.; Clarkson, P. A.; Gandarias, M. L.; Medina, E.
2001
New similarity solutions of the unsteady incompressible boundary-layer equations. Zbl 1003.76019
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
2000
Hierarchies of exact solutions for the discrete third Painlevé equation. Zbl 1115.34302
Clarkson, Peter A.; Webster, Helen N.
2000
On the relation between the continuous and discrete Painlevé equations. Zbl 0994.34077
Klarkson, P. A.; Mansfield, E. L.; Webster, H. N.
2000
Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach. Zbl 0923.35170
Clarkson, Peter A.; Joshi, Nalini; Pickering, Andrew
1999
Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations. Zbl 1136.76342
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
1999
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
1999
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
1999
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
1999
Symmetries and integrability of difference equations. Proceedings of the 2nd international conference, Canterbury, UK, July 1–5, 1996. Zbl 0910.00045
1999
Application of uniform asymptotics to the second Painlevé transcendent. Zbl 0912.34007
Bassom, Andrew P.; Clarkson, Peter A.; Law, C. K.; McLeod, J. Bryce
1998
Nonclassical reductions of a $$(3+1)$$-cubic nonlinear Schrödinger system. Zbl 0996.35069
Mansfield, Elizabeth L.; Reid, Gregory J.; Clarkson, Peter A.
1998
Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Zbl 0931.35125
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
1998
Shallow water wave systems. Zbl 1020.35083
Clarkson, Peter A.; Priestley, Thomas J.
1998
Bäcklund transformations and nonlinear superposition formulae of a differential-difference KdV equation. Zbl 0947.37051
Hu, Xingbao; Clarkson, Peter A.
1998
Multicomponent equations associated to non-isospectral scattering problems. Zbl 0889.35094
Clarkson, Peter A.; Gordoa, Pilar R.; Pickering, Andrew
1997
Bäcklund transformations and solution hierarchies for the third Painlevé equation. Zbl 0878.34006
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
Symmetries of a class of nonlinear third-order partial differential equations. Zbl 0879.35005
Clarkson, P. A.; Mansfield, E. L.; Priestley, T. J.
1997
New integrable differential-difference systems. Zbl 0924.35157
Hu, Xing-Biao; Clarkson, Peter A.; Bullough, Robin
1997
Symmetries and exact solutions for a $$2+1$$-dimensional shallow water wave equation. Zbl 0869.68060
Mansfield, Elizabeth L.; Clarkson, Peter A.
1997
The classical, direct, and nonclassical methods for symmetry reductions of nonlinear partial differential equations. Zbl 0901.58069
Clarkson, Peter A.; Ludlow, David K.; Priestley, Thomas J.
1997
Application of the isomonodromy deformation method to the fourth Painlevé equation. Zbl 0872.35108
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
1996
Symmetries and exact solutions of a $$(2+1)$$-dimensional sine-Gordon system. Zbl 0862.35104
Clarkson, Peter A.; Mansfield, Elizabeth L.; Milne, Alice E.
1996
On the application of solutions of the fourth Painlevé equation to various physically motivated nonlinear partial differential equations. Zbl 0845.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
1996
Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation. Zbl 0868.35132
Hu, Xing-Biao; Clarkson, Peter A.
1995
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
1995
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Zbl 0846.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
1995
Symmetry reductions and exact solutions of shallow water wave equations. Zbl 0835.35006
Clarkson, Peter A.; Mansfield, Elizabeth L.
1995
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 0952.37019
Clarkson, Peter A.
1995
Symmetry reductions and exact solutions of a class of nonlinear heat equations. Zbl 0812.35017
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
Algorithms for the nonclassical method of symmetric reductions. Zbl 0823.58036
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
On a shallow water wave equation. Zbl 0803.35111
Clarkson, Peter A.; Mansfield, Elizabeth L.
1994
New symmetry reductions and exact solutions of the Davey-Stewartson system. I: Reductions to ordinary differential equations. Zbl 0802.76009
Clarkson, Peter A.; Hood, Simon
1994
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
1994
New exact solutions of the discrete fourth Painlevé equation. Zbl 0941.39502
Bassom, Andrew P.; Clarkson, Peter A.
1994
Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations. Zbl 0788.35067
Clarkson, P. A.; Mansfield, E. L.
1993
Nonclassical symmetry reductions of nonlinear partial differential equations. Zbl 0805.35092
Clarkson, P. A.
1993
Numerical studies of the fourth Painlevé equation. Zbl 0782.65099
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.
1993
Symmetry reductions of a generalized, cylindrical nonlinear Schrödinger equation. Zbl 0772.35065
Clarkson, Peter A.; Hood, Simon
1993
Rational solutions and Bäcklund transformations for the third Painlevé equation. Zbl 0794.34001
Milne, A. E.; Clarkson, P. A.
1993
Symmetry reductions and exact solutions for a generalised Boussinesq equation. Zbl 0793.35076
Ludlow, D. K.; Clarkson, P. A.
1993
Symmetry reductions and exact solutions of the Davey-Stewartson system. Zbl 0793.35100
Hood, S.; Clarkson, P. A.
1993
A study of the fourth Painlevé equation. Zbl 0793.35099
Hicks, A. C.; Clarkson, P. A.; Bassom, A. P.
1993
Symmetries of the nonlinear heat equation. Zbl 0805.35049
Clarkson, Peter A.; Mansfield, Elizabeth L.
1993
The Painlevé-Kowalevski and poly-Painlevé tests for integrability. Zbl 0803.35128
Kruskal, Martin D.; Clarkson, Peter A.
1992
Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation. Zbl 0752.35064
Clarkson, Peter A.
1992
Integral equations and exact solutions for the fourth Painlevé equation. Zbl 0751.34002
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.; McLeod, J. B.
1992
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya- Khokhlov equation. Zbl 0771.35053
Clarkson, Peter A.; Hood, Simon
1992
Integral equations and connection formulae for the Painlevé equations. Zbl 0856.34009
Clarkson, P. A.; McLeod, J. B.
1992
Solitons, nonlinear evolution equations and inverse scattering. Zbl 0762.35001
Ablowitz, M. J.; Clarkson, P. A.
1991
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Zbl 0734.35123
Clarkson, P. A.; Winternitz, P.
1991
Exact solutions of the multidimensional derivative nonlinear Schrödinger equation for many-body systems near criticality. Zbl 0738.35090
Clarkson, Peter A.; Tuszyński, J. A.
1990
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
1990
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
1990
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
1990
New similarity reductions of the Boussinesq equation. Zbl 0698.35137
Clarkson, Peter A.; Kruskal, Martin D.
1989
New similarity reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations. Zbl 0711.35113
Clarkson, Peter A.
1989
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
1989
...and 8 more Documents
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### Cited by 2,812 Authors

 91 Zhang, Hongqing 69 Ma, Wen-Xiu 58 Yan, Zhenya 54 Tian, Bo 46 Tian, Shoufu 44 Chen, Yong 40 Gao, Yitian 40 Kudryashov, Nikolaĭ Alekseevich 39 Wazwaz, Abdul-Majid Abdul-Rahman 38 Clarkson, Peter A. 36 Zhang, Sheng 32 Zhang, Tiantian 28 Fan, Engui 26 Lü, Xing 26 Xia, Tie-Cheng 25 Lou, Senyue 24 Khalique, Chaudry Masood 24 Li, Biao 23 Dai, Zhengde 22 He, Jingsong 22 Qu, Changzheng 21 Gandarias Núñez, Maria Luz 21 Li, Jibin 21 Liu, Hanze 21 Wen, Xiaoyong 20 Wang, Qi 20 Zhang, Yufeng 19 Bekir, Ahmet 19 Wang, Xiubin 19 Yu, Fajun 19 Zhang, Haiqiang 18 Ablowitz, Mark Jay 18 Rogers, Colin 16 Chen, Dengyuan 16 Song, Lina 15 Bruzón, Maria Santos 15 Filipuk, Galina V. 15 Yu, Xin 15 Zayed, Elsayed M. E. 14 Geng, Xianguo 14 Inc, Mustafa 14 Liu, Wenjun J. 14 Winternitz, Pavel 14 Xu, Guiqiong 13 Hu, Xingbiao 13 Shen, Shoufeng 12 Broadbridge, Philip 12 Grundland, Alfred Michel 12 Huang, Dingjiang 12 Meng, Xianghua 12 Popovych, Roman O. 12 Xin, Xiangpeng 12 Xu, Tao 11 Ma, Zhengyi 11 Manafian Heris, Jalil 11 Mihalache, Dumitru 11 Soliman, Ahmed Abo-Elmagd 11 Vitanov, Nikolay K. 11 Wang, Chuanjian 11 Wang, Mingliang 11 Yusufoğlu (Agadjanov), Elçin 10 Biswas, Anjan 10 Bratsos, Athanassios G. 10 Dimitrova, Zlatinka I. 10 Gordoa, Pilar Ruiz 10 Guha, Partha 10 Li, Zitian 10 Malomed, Boris A. 10 Shan, Wenrui 10 Tang, Shengqiang 10 Tian, Lixin 10 Wang, Dengshan 10 Yomba, Emmanuel 10 Zhang, Weiguo 10 Zhaqilao, Z. 9 Bai, Chenglin 9 Demina, Maria V. 9 Liu, Xiqiang 9 Luo, Lin 9 Maccari, Attilio 9 Mansfield, Elizabeth Louise 9 Mei, Jianqin 9 Seadawy, Aly R. 9 Shang, Yadong 9 Sun, Zhiyuan 9 Wang, Lei 9 Yang, Jianke 9 Yong, Xuelin 8 Chen, Junchao 8 Conte, Robert Maurice 8 Dai, Chaoqing 8 Dubrovsky, V. G. 8 Fokas, Athanassios S. 8 Govinder, Keshlan Sathasiva 8 Hereman, Willy A. 8 Ji, Lina 8 Jiang, Yan 8 Joshi, Nalini 8 Kevrekidis, Panayotis G. 8 Konopelchenko, Boris Georgievich ...and 2,712 more Authors
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### Cited in 301 Serials

 278 Applied Mathematics and Computation 221 Chaos, Solitons and Fractals 181 Physics Letters. A 152 Journal of Mathematical Physics 118 Communications in Nonlinear Science and Numerical Simulation 95 Applied Mathematics Letters 94 Nonlinear Dynamics 90 Computers & Mathematics with Applications 90 Journal of Mathematical Analysis and Applications 83 Physica D 53 Journal of Nonlinear Mathematical Physics 50 Theoretical and Mathematical Physics 44 Studies in Applied Mathematics 40 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 29 Journal of Differential Equations 29 Abstract and Applied Analysis 29 Advances in Mathematical Physics 28 International Journal of Modern Physics B 28 Journal of Geometry and Physics 27 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 25 Wave Motion 25 Advances in Difference Equations 23 Acta Applicandae Mathematicae 22 Communications in Mathematical Physics 19 Mathematical Problems in Engineering 18 Mathematics and Computers in Simulation 18 Mathematical and Computer Modelling 18 Nonlinear Analysis. Real World Applications 17 International Journal of Theoretical Physics 17 Reports on Mathematical Physics 17 Journal of Computational and Applied Mathematics 16 Communications in Theoretical Physics 15 Letters in Mathematical Physics 15 Regular and Chaotic Dynamics 15 East Asian Journal on Applied Mathematics 15 International Journal of Applied and Computational Mathematics 14 Physica A 14 Applied Mathematics and Mechanics. (English Edition) 13 Nonlinearity 13 Journal of Nonlinear Science 13 Chaos 12 Computer Physics Communications 12 Mathematical Methods in the Applied Sciences 12 Journal of Applied Mathematics 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Annals of Physics 11 International Journal of Nonlinear Sciences and Numerical Simulation 11 Journal of Physics A: Mathematical and Theoretical 10 Acta Mechanica 10 Acta Mathematicae Applicatae Sinica. English Series 10 Journal of Symbolic Computation 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Journal of the Egyptian Mathematical Society 10 Complexity 9 Nuclear Physics. B 9 Numerical Methods for Partial Differential Equations 9 Analysis and Mathematical Physics 8 Proceedings of the American Mathematical Society 8 European Journal of Applied Mathematics 8 Symmetry 7 Ricerche di Matematica 7 Constructive Approximation 7 Applied Mathematical Modelling 7 International Journal of Computer Mathematics 7 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 7 Discrete Dynamics in Nature and Society 7 Differential Equations 7 Analysis and Applications (Singapore) 7 Random Matrices: Theory and Applications 7 Journal of Applied Analysis and Computation 7 AIMS Mathematics 6 SIAM Journal on Mathematical Analysis 6 Journal of Difference Equations and Applications 6 Discrete and Continuous Dynamical Systems 6 Qualitative Theory of Dynamical Systems 6 Physical Review Letters 6 Waves in Random and Complex Media 5 Modern Physics Letters A 5 Applicable Analysis 5 International Journal of Engineering Science 5 Journal of Engineering Mathematics 5 Ukrainian Mathematical Journal 5 Advances in Mathematics 5 Journal of Approximation Theory 5 Transactions of the American Mathematical Society 5 Applied Numerical Mathematics 5 Differential Geometry and its Applications 5 Bulletin of the American Mathematical Society. New Series 5 Applied Mathematics. Series B (English Edition) 5 Journal of Mathematical Sciences (New York) 5 Computational and Applied Mathematics 5 International Journal of Modern Physics C 5 The ANZIAM Journal 5 Boundary Value Problems 5 Science China. Mathematics 5 Nonlinear Analysis. Theory, Methods & Applications 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 International Journal of Modern Physics A 4 Journal of Computational Physics 4 Physics Letters. B ...and 201 more Serials
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### Cited in 55 Fields

 2,235 Partial differential equations (35-XX) 1,014 Dynamical systems and ergodic theory (37-XX) 345 Ordinary differential equations (34-XX) 295 Fluid mechanics (76-XX) 239 Numerical analysis (65-XX) 167 Quantum theory (81-XX) 151 Special functions (33-XX) 121 Computer science (68-XX) 115 Global analysis, analysis on manifolds (58-XX) 73 Optics, electromagnetic theory (78-XX) 71 Statistical mechanics, structure of matter (82-XX) 62 Mechanics of deformable solids (74-XX) 61 Difference and functional equations (39-XX) 51 Mechanics of particles and systems (70-XX) 42 Differential geometry (53-XX) 39 Operator theory (47-XX) 36 Relativity and gravitational theory (83-XX) 35 Functions of a complex variable (30-XX) 32 Algebraic geometry (14-XX) 32 Nonassociative rings and algebras (17-XX) 32 Harmonic analysis on Euclidean spaces (42-XX) 28 Probability theory and stochastic processes (60-XX) 24 Biology and other natural sciences (92-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 22 Topological groups, Lie groups (22-XX) 20 Integral equations (45-XX) 19 Geophysics (86-XX) 18 Approximations and expansions (41-XX) 16 Real functions (26-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Classical thermodynamics, heat transfer (80-XX) 10 Number theory (11-XX) 9 Commutative algebra (13-XX) 8 Functional analysis (46-XX) 7 General and overarching topics; collections (00-XX) 6 Combinatorics (05-XX) 5 History and biography (01-XX) 5 Field theory and polynomials (12-XX) 5 Integral transforms, operational calculus (44-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Astronomy and astrophysics (85-XX) 4 Systems theory; control (93-XX) 3 Group theory and generalizations (20-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Measure and integration (28-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Geometry (51-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)