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## Clarkson, Peter A.

Compute Distance To:
 Author ID: clarkson.peter-a Published as: Clarkson, P. A.; Clarkson, Peter; Clarkson, Peter A.; Klarkson, P. A. Homepage: https://www.kent.ac.uk/mathematics-statistics-actuarial-science/people/404/www.k... External Links: MGP · Math-Net.Ru · ORCID · dblp
 Documents Indexed: 122 Publications since 1982, including 3 Books
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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 Joshi, Nalini 4 Milne, Alice E. 4 Priestley, Thomas J. 3 Hone, Andrew N. W. 3 Jordaan, Kerstin 3 Rogers, Colin 3 Webster, Helen N. 2 Ankiewicz, Adrian 2 Cosgrove, Christopher M. 2 Dowie, Ellen 2 Hu, Xingbao 2 Kruskal, Martin David 2 Mazzocco, Marta 2 Nijhoff, Frank W. 2 Olver, Peter John 2 Pickering, Andrew 2 Sen, Ayan 2 Winternitz, Pavel 1 Akhmediev, Nail N. 1 Bîlă, Nicoleta Virginia 1 Bruzón, Maria Santos 1 Bullough, Robin K. 1 Chakravarty, Sarbarish 1 Chakravarty, Sarby 1 Chiu, Tin Lok 1 Chow, Kwok Wing 1 Estévez, Pilar G. 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 Kelil, Abey 1 Law, Chun-Kong 1 LeVeque, Randall J. 1 Liu, Tianyang 1 Loureiro, Ana Filipa 1 Medina, Enrique A. 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 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) 51 Ordinary differential equations (34-XX) 35 Dynamical systems and ergodic theory (37-XX) 29 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 3,377 times in 2,672 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
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
1995
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
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
Painlevé equations – nonlinear special functions. Zbl 1100.33006
Clarkson, Peter A.
2006
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Zbl 0734.35123
Clarkson, P. A.; Winternitz, P.
1991
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
1990
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
1989
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 reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations. Zbl 0711.35113
Clarkson, Peter A.
1989
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
2003
Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations. Zbl 0788.35067
Clarkson, P. A.; Mansfield, E. L.
1993
Hodograph transformations of linearizable partial differential equations. Zbl 0694.35005
Clarkson, P. A.; Fokas, A. S.; Ablowitz, M. J.
1989
Rogue waves, rational solutions, the patterns of their zeros and integral relations. Zbl 1189.35300
Ankiewicz, Adrian; Clarkson, Peter A.; Akhmediev, Nail
2010
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
2003
Multicomponent equations associated to non-isospectral scattering problems. Zbl 0889.35094
Clarkson, Peter A.; Gordoa, Pilar R.; Pickering, Andrew
1997
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
1990
Vortices and polynomials. Zbl 1372.37110
Clarkson, P. A.
2009
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
Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation. Zbl 0752.35064
Clarkson, Peter A.
1992
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
The fourth Painlevé equation and associated special polynomials. Zbl 1063.33029
Clarkson, Peter A.
2003
Bäcklund transformations and solution hierarchies for the third Painlevé equation. Zbl 0878.34006
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Zbl 0846.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
1995
A connection formula for the second Painlevé transcendent. Zbl 0653.34020
Clarkson, Peter A.; McLeod, J. Bryce
1988
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
Symmetry reductions and exact solutions of shallow water wave equations. Zbl 0835.35006
Clarkson, Peter A.; Mansfield, Elizabeth L.
1995
Remarks on the Yablonskii-Vorob’ev polynomials. Zbl 1053.34082
Clarkson, Peter A.
2003
Rational solutions of the Boussinesq equation and applications to rogue waves. Zbl 1403.37073
Clarkson, Peter A.; Dowie, Ellen
2017
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 0952.37019
Clarkson, Peter A.
1995
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
Painlevé analysis of the damped, driven nonlinear Schrödinger equation. Zbl 0681.35077
Clarkson, Peter A.
1988
The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation. Zbl 1321.34115
Clarkson, Peter A.; Jordaan, Kerstin
2014
Symmetries of a class of nonlinear third-order partial differential equations. Zbl 0879.35005
Clarkson, P. A.; Mansfield, E. L.; Priestley, T. J.
1997
Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations. Zbl 1112.33015
Clarkson, Peter A.
2006
The thrid Painlevé equation and associated special polynomials. Zbl 1046.33015
Clarkson, Peter A.
2003
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
Properties of generalized Freud polynomials. Zbl 1437.33011
Clarkson, Peter A.; Jordaan, Kerstin
2018
A generalized Freud weight. Zbl 1336.33022
Clarkson, Peter A.; Jordaan, Kerstin; Kelil, Abey
2016
Symmetry group analysis of the shallow water and semi-geostrophic equations. Zbl 1088.76059
Bîlă, Nicoleta; Mansfield, Elizabeth L.; Clarkson, Peter A.
2006
Special polynomials associated with rational solutions of the fifth Painlevé equation. Zbl 1077.33035
Clarkson, Peter A.
2005
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
1999
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
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
Nonclassical symmetry reductions of nonlinear partial differential equations. Zbl 0805.35092
Clarkson, P. A.
1993
New similarity solutions of the unsteady incompressible boundary-layer equations. Zbl 1003.76019
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
2000
Numerical studies of the fourth Painlevé equation. Zbl 0782.65099
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.
1993
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya- Khokhlov equation. Zbl 0771.35053
Clarkson, Peter A.; Hood, Simon
1992
On Airy solutions of the second Painlevé equation. Zbl 1346.35179
Clarkson, Peter A.
2016
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Zbl 1275.34109
Clarkson, Peter A.
2013
The symmetric fourth Painlevé hierarchy and associated special polynomials. Zbl 1202.34155
Filipuk, Galina V.; Clarkson, Peter A.
2008
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
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
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
On rational solutions of the fourth Painlevé equation and its Hamiltonian. Zbl 1091.34052
Clarkson, P. A.
2005
Nonclassical reductions of a $$(3+1)$$-cubic nonlinear Schrödinger system. Zbl 0996.35069
Mansfield, Elizabeth L.; Reid, Gregory J.; Clarkson, Peter A.
1998
New integrable differential-difference systems. Zbl 0924.35157
Hu, Xing-Biao; Clarkson, Peter A.; Bullough, Robin
1997
Integrability of Klein-Gordon equations. Zbl 0629.35104
Clarkson, Peter A.; McLeod, J. Bryce; Olver, Peter J.; Ramani, Alfred
1986
The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation. Zbl 0616.35080
Clarkson, Peter A.
1986
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
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
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
1999
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
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
1999
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
Rational solutions and Bäcklund transformations for the third Painlevé equation. Zbl 0794.34001
Milne, A. E.; Clarkson, P. A.
1993
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
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
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
2017
Asymptotics of the second Painlevé equation. Zbl 1185.33027
Clarkson, Peter A.
2008
On the Lax pairs of the symmetric Painlevé equations. Zbl 1145.34380
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
2006
Rational solutions of an extended Lotka-Volterra equation. Zbl 1362.34099
Hu, X. B.; Clarkson, P. A.
2002
Application of the isomonodromy deformation method to the fourth Painlevé equation. Zbl 0872.35108
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
1997
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
New exact solutions of the discrete fourth Painlevé equation. Zbl 0941.39502
Bassom, Andrew P.; Clarkson, Peter A.
1994
Symmetry reductions and exact solutions for a generalised Boussinesq equation. Zbl 0793.35076
Ludlow, D. K.; Clarkson, P. A.
1993
Integral equations and connection formulae for the Painlevé equations. Zbl 0856.34009
Clarkson, P. A.; McLeod, J. B.
1992
Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests. Zbl 0591.35061
Clarkson, Peter A.
1985
Open problems for Painlevé equations. Zbl 1416.33028
Clarkson, Peter A.
2019
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
2017
Rational solutions of the classical Boussinesq system. Zbl 1179.35282
Clarkson, Peter A.
2009
Rational solutions of the Boussinesq equation. Zbl 1173.33315
Clarkson, Peter A.
2008
Special polynomials associated with rational and algebraic solutions of the Painlevé equations. Zbl 1165.34057
Clarkson, Peter A.
2006
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
Shallow water wave systems. Zbl 1020.35083
Clarkson, Peter A.; Priestley, Thomas J.
1998
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
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
2017
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
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
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
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
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
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
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
2003
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
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
On discrete Painlevé equations as Bäcklund transformations. Zbl 0991.39008
Clarkson, P. A.; Mansfield, E. L.; Webster, H. N.
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
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
1999
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
1999
Symmetries and integrability of difference equations. Proceedings of the 2nd international conference, Canterbury, UK, July 1–5, 1996. Zbl 0910.00045
Clarkson, Peter A. (ed.); Nijhoff, Frank W. (ed.)
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
Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation and their application to discrete equations. Zbl 0862.34003
Clarkson, Peter A.; Bassom, Andrew P.
1996
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
1995
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
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
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
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
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
Symmetries of the nonlinear heat equation. Zbl 0805.35049
Clarkson, Peter A.; Mansfield, Elizabeth L.
1993
A study of the fourth Painlevé equation. Zbl 0793.35099
Hicks, A. C.; Clarkson, P. A.; Bassom, A. P.
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
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
1990
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
1990
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
1990
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 of the Boussinesq equation. Zbl 0698.35137
Clarkson, Peter A.; Kruskal, Martin D.
1989
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
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
...and 8 more Documents
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#### Cited by 2,676 Authors

 93 Zhang, Hongqing 63 Ma, Wen-Xiu 53 Tian, Bo 52 Yan, Zhenya 44 Tian, Shoufu 42 Kudryashov, Nikolaĭ Alekseevich 41 Chen, Yong 39 Gao, Yitian 36 Clarkson, Peter A. 36 Wazwaz, Abdul-Majid Abdul-Rahman 34 Zhang, Sheng 32 Zhang, Tiantian 27 Lü, Xing 27 Xia, Tie-Cheng 25 Lou, Senyue 24 Fan, Engui 23 Dai, Zhengde 23 Li, Biao 23 Wang, Qi 22 Qu, Changzheng 21 Bekir, Ahmet 21 Khalique, Chaudry Masood 20 Li, Jibin 19 Gandarias Núñez, Maria Luz 19 He, Jingsong 19 Rogers, Colin 19 Wen, Xiaoyong 18 Wang, Xiubin 18 Yu, Fajun 17 Ablowitz, Mark Jay 17 Chen, Dengyuan 17 Zhang, Haiqiang 16 Estévez, Pilar G. 16 Song, Lina 16 Yu, Xin 15 Bruzón, Maria Santos 15 Filipuk, Galina V. 15 Liu, Wenjun J. 15 Winternitz, Pavel 15 Zayed, Elsayed M. E. 14 Liu, Hanze 14 Shen, Shoufeng 13 Meng, Xianghua 13 Xu, Guiqiong 12 Broadbridge, Philip 12 Grundland, Alfred Michel 12 Huang, Dingjiang 12 Inc, Mustafa 12 Zhang, Yufeng 11 Geng, Xianguo 11 Hu, Xingbiao 11 Ma, Zhengyi 11 Popovych, Roman O. 11 Soliman, Ahmed Abo-Elmagd 11 Vitanov, Nikolay K. 11 Wang, Chuanjian 11 Wang, Lei 11 Wang, Mingliang 11 Yusufoğlu (Agadjanov), Elçin 10 Biswas, Anjan 10 Bratsos, Athanassios G. 10 Dimitrova, Zlatinka I. 10 Guha, Partha 10 Li, Zitian 10 Mihalache, Dumitru 10 Sun, Zhiyuan 10 Tang, Shengqiang 10 Wang, Dengshan 10 Yomba, Emmanuel 9 Chakravarty, Sarbarish 9 Dai, Chaoqing 9 Gordoa, Pilar Ruiz 9 Liu, Xiqiang 9 Maccari, Attilio 9 Mei, Jianqin 9 Meng, Dexin 9 Sun, Yepeng 9 Xie, Fuding 9 Xu, Tao 9 Zhang, Weiguo 9 Zhaqilao, Z. 8 Conte, Robert M. 8 Demina, Maria V. 8 Hereman, Willy A. 8 Jiang, Yan 8 Joshi, Nalini 8 Li, Zhibin 8 Lu, Dianchen 8 Lü, Zhuosheng 8 Luo, Lin 8 Malomed, Boris A. 8 Mansfield, Elizabeth Louise 8 Santini, Paolo Maria 8 Schief, Wolfgang Karl 8 Shang, Yadong 8 Sun, Wen-Rong 8 Tian, Lixin 8 Xu, Xixiang 8 Yong, Xuelin 8 Zhang, Jinliang ...and 2,576 more Authors
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#### Cited in 271 Serials

 280 Applied Mathematics and Computation 225 Chaos, Solitons and Fractals 174 Physics Letters. A 151 Journal of Mathematical Physics 112 Communications in Nonlinear Science and Numerical Simulation 94 Nonlinear Dynamics 93 Computers & Mathematics with Applications 90 Journal of Mathematical Analysis and Applications 76 Applied Mathematics Letters 65 Physica D 52 Journal of Nonlinear Mathematical Physics 44 Theoretical and Mathematical Physics 44 Studies in Applied Mathematics 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 30 Abstract and Applied Analysis 27 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 25 International Journal of Modern Physics B 24 Journal of Differential Equations 23 Acta Applicandae Mathematicae 22 Advances in Mathematical Physics 21 Communications in Mathematical Physics 19 Reports on Mathematical Physics 19 Wave Motion 19 Journal of Geometry and Physics 19 Mathematical Problems in Engineering 18 Mathematical and Computer Modelling 17 International Journal of Theoretical Physics 17 Journal of Computational and Applied Mathematics 17 Nonlinear Analysis. Real World Applications 17 Advances in Difference Equations 16 Mathematics and Computers in Simulation 16 Communications in Theoretical Physics 14 Applied Mathematics and Mechanics. (English Edition) 14 Annals of Physics 14 Regular and Chaotic Dynamics 13 Chaos 12 Computer Physics Communications 12 Letters in Mathematical Physics 12 Mathematical Methods in the Applied Sciences 12 Nonlinearity 12 Journal of Applied Mathematics 11 Physica A 11 Journal of Physics A: Mathematical and Theoretical 11 East Asian Journal on Applied Mathematics 10 Acta Mechanica 10 Acta Mathematicae Applicatae Sinica. English Series 10 Journal of the Egyptian Mathematical Society 10 Complexity 9 Numerical Methods for Partial Differential Equations 9 Journal of Nonlinear Science 9 International Journal of Applied and Computational Mathematics 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Journal of Symbolic Computation 8 European Journal of Applied Mathematics 8 Applied Mathematical Modelling 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Symmetry 7 Nuclear Physics. B 7 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 7 Analysis and Applications (Singapore) 7 Random Matrices: Theory and Applications 7 Journal of Applied Analysis and Computation 6 Proceedings of the American Mathematical Society 6 Constructive Approximation 6 Discrete and Continuous Dynamical Systems 6 International Journal of Nonlinear Sciences and Numerical Simulation 6 Physical Review Letters 6 Differential Equations 5 Modern Physics Letters A 5 Applicable Analysis 5 International Journal of Engineering Science 5 Physics Letters. B 5 Journal of Approximation Theory 5 Ricerche di Matematica 5 Transactions of the American Mathematical Society 5 Applied Numerical Mathematics 5 SIAM Journal on Mathematical Analysis 5 Bulletin of the American Mathematical Society. New Series 5 Applied Mathematics. Series B (English Edition) 5 Journal of Difference Equations and Applications 5 Discrete Dynamics in Nature and Society 5 International Journal of Modern Physics C 5 The ANZIAM Journal 5 Science China. Mathematics 5 Nonlinear Analysis. Theory, Methods & Applications 4 International Journal of Modern Physics A 4 Journal of Computational Physics 4 Journal of Engineering Mathematics 4 Ukrainian Mathematical Journal 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Advances in Mathematics 4 Science in China. Series A 4 Differential Geometry and its Applications 4 Computational Mathematics and Mathematical Physics 4 Journal of Mathematical Sciences (New York) 4 Journal of Applied Mathematics and Computing 4 International Journal of Geometric Methods in Modern Physics 4 Foundations of Physics 4 Boundary Value Problems 3 Communications on Pure and Applied Mathematics ...and 171 more Serials
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#### Cited in 53 Fields

 2,067 Partial differential equations (35-XX) 940 Dynamical systems and ergodic theory (37-XX) 313 Ordinary differential equations (34-XX) 264 Fluid mechanics (76-XX) 228 Numerical analysis (65-XX) 148 Quantum theory (81-XX) 135 Special functions (33-XX) 112 Global analysis, analysis on manifolds (58-XX) 108 Computer science (68-XX) 61 Statistical mechanics, structure of matter (82-XX) 58 Mechanics of deformable solids (74-XX) 56 Difference and functional equations (39-XX) 54 Optics, electromagnetic theory (78-XX) 44 Mechanics of particles and systems (70-XX) 38 Differential geometry (53-XX) 36 Operator theory (47-XX) 31 Relativity and gravitational theory (83-XX) 30 Algebraic geometry (14-XX) 30 Functions of a complex variable (30-XX) 28 Nonassociative rings and algebras (17-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 27 Probability theory and stochastic processes (60-XX) 20 Biology and other natural sciences (92-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 19 Topological groups, Lie groups (22-XX) 18 Integral equations (45-XX) 17 Geophysics (86-XX) 13 Real functions (26-XX) 11 Approximations and expansions (41-XX) 10 Number theory (11-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Commutative algebra (13-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Functional analysis (46-XX) 6 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 Calculus of variations and optimal control; optimization (49-XX) 4 Astronomy and astrophysics (85-XX) 4 Systems theory; control (93-XX) 3 Integral transforms, operational calculus (44-XX) 3 Algebraic topology (55-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Statistics (62-XX) 1 Mathematical logic and foundations (03-XX) 1 $$K$$-theory (19-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)