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Clarkson, Peter A.

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Author ID: clarkson.peter-a Recent zbMATH articles by "Clarkson, Peter A."
Published as: Clarkson, Peter A.; Clarkson, P. A.; Clarkson, Peter; Klarkson, P. A.
Homepage: https://www.kent.ac.uk/mathematics-statistics-actuarial-science/people/404/www.k...
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Documents Indexed: 123 Publications since 1982, including 3 Books
all top 5

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

Publications by Year

Citations contained in zbMATH Open

107 Publications have been cited 3,368 times in 2,690 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.
271
1989
Symmetry reductions and exact solutions of a class of nonlinear heat equations. Zbl 0812.35017
Clarkson, Peter A.; Mansfield, Elizabeth L.
80
1994
Solitary-wave interactions in elastic rods. Zbl 0606.73028
Clarkson, Peter A.; LeVeque, Randall J.; Saxton, Ralph
57
1986
Painlevé analysis of the nonlinear Schrödinger family of equations. Zbl 0632.35073
Clarkson, Peter A.; Cosgrove, Christopher M.
45
1987
Algorithms for the nonclassical method of symmetric reductions. Zbl 0823.58036
Clarkson, Peter A.; Mansfield, Elizabeth L.
40
1994
On a shallow water wave equation. Zbl 0803.35111
Clarkson, Peter A.; Mansfield, Elizabeth L.
37
1994
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
37
1996
Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach. Zbl 0923.35170
Clarkson, Peter A.; Joshi, Nalini; Pickering, Andrew
35
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.
32
1995
Painlevé equations – nonlinear special functions. Zbl 1100.33006
Clarkson, Peter A.
31
2006
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
31
1995
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Zbl 0734.35123
Clarkson, P. A.; Winternitz, P.
30
1991
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
29
1989
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
29
1990
The Painlevé-Kowalevski and poly-Painlevé tests for integrability. Zbl 0803.35128
Kruskal, Martin D.; Clarkson, Peter A.
29
1992
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
29
1990
Hodograph transformations of linearizable partial differential equations. Zbl 0694.35005
Clarkson, P. A.; Fokas, A. S.; Ablowitz, M. J.
26
1989
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
26
2003
New similarity reductions and Painlevé analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations. Zbl 0711.35113
Clarkson, Peter A.
25
1989
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
24
2003
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
24
1990
Vortices and polynomials. Zbl 1372.37110
Clarkson, P. A.
24
2009
Multicomponent equations associated to non-isospectral scattering problems. Zbl 0889.35094
Clarkson, Peter A.; Gordoa, Pilar R.; Pickering, Andrew
23
1997
Exact solutions of the multidimensional derivative nonlinear Schrödinger equation for many-body systems near criticality. Zbl 0738.35090
Clarkson, Peter A.; Tuszyński, J. A.
23
1990
Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations. Zbl 0788.35067
Clarkson, P. A.; Mansfield, E. L.
22
1993
Rogue waves, rational solutions, the patterns of their zeros and integral relations. Zbl 1189.35300
Ankiewicz, Adrian; Clarkson, Peter A.; Akhmediev, Nail
22
2010
Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation. Zbl 0752.35064
Clarkson, Peter A.
21
1992
The fourth Painlevé equation and associated special polynomials. Zbl 1063.33029
Clarkson, Peter A.
19
2003
Symmetries and exact solutions of a \((2+1)\)-dimensional sine-Gordon system. Zbl 0862.35104
Clarkson, Peter A.; Mansfield, Elizabeth L.; Milne, Alice E.
19
1996
A connection formula for the second Painlevé transcendent. Zbl 0653.34020
Clarkson, Peter A.; McLeod, J. Bryce
18
1988
Symmetry reductions and exact solutions of shallow water wave equations. Zbl 0835.35006
Clarkson, Peter A.; Mansfield, Elizabeth L.
18
1995
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Zbl 0846.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
18
1995
Bäcklund transformations and solution hierarchies for the third Painlevé equation. Zbl 0878.34006
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
18
1997
Application of uniform asymptotics to the second Painlevé transcendent. Zbl 0912.34007
Bassom, Andrew P.; Clarkson, Peter A.; Law, C. K.; McLeod, J. Bryce
18
1998
The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation. Zbl 1321.34115
Clarkson, Peter A.; Jordaan, Kerstin
18
2014
Rational solutions of the Boussinesq equation and applications to rogue waves. Zbl 1403.37073
Clarkson, Peter A.; Dowie, Ellen
17
2017
Remarks on the Yablonskii-Vorob’ev polynomials. Zbl 1053.34082
Clarkson, Peter A.
16
2003
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 0952.37019
Clarkson, Peter A.
15
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.
14
1992
Painlevé analysis of the damped, driven nonlinear Schrödinger equation. Zbl 0681.35077
Clarkson, Peter A.
13
1988
Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations. Zbl 1112.33015
Clarkson, Peter A.
13
2006
A generalized Freud weight. Zbl 1336.33022
Clarkson, Peter A.; Jordaan, Kerstin; Kelil, Abey
13
2016
Symmetries of a class of nonlinear third-order partial differential equations. Zbl 0879.35005
Clarkson, P. A.; Mansfield, E. L.; Priestley, T. J.
12
1997
Nonclassical symmetry reductions of nonlinear partial differential equations. Zbl 0805.35092
Clarkson, P. A.
11
1993
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.
11
1999
The thrid Painlevé equation and associated special polynomials. Zbl 1046.33015
Clarkson, Peter A.
11
2003
Symmetry group analysis of the shallow water and semi-geostrophic equations. Zbl 1088.76059
Bîlă, Nicoleta; Mansfield, Elizabeth L.; Clarkson, Peter A.
11
2006
Properties of generalized Freud polynomials. Zbl 1437.33011
Clarkson, Peter A.; Jordaan, Kerstin
11
2018
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
10
1994
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
10
1994
New similarity solutions of the unsteady incompressible boundary-layer equations. Zbl 1003.76019
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
10
2000
Special polynomials associated with rational solutions of the fifth Painlevé equation. Zbl 1077.33035
Clarkson, Peter A.
10
2005
Numerical studies of the fourth Painlevé equation. Zbl 0782.65099
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.
9
1993
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
9
1999
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya- Khokhlov equation. Zbl 0771.35053
Clarkson, Peter A.; Hood, Simon
9
1992
On Airy solutions of the second Painlevé equation. Zbl 1346.35179
Clarkson, Peter A.
9
2016
The symmetric fourth Painlevé hierarchy and associated special polynomials. Zbl 1202.34155
Filipuk, Galina V.; Clarkson, Peter A.
8
2008
Integrability of Klein-Gordon equations. Zbl 0629.35104
Clarkson, Peter A.; McLeod, J. Bryce; Olver, Peter J.; Ramani, Alfred
7
1986
Open problems in symmetry analysis. Zbl 1172.35306
Clarkson, Peter A.; Mansfield, Elizabeth L.
7
2001
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
7
2006
Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation. Zbl 1126.35062
Clarkson, Peter A.
7
2006
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Zbl 1275.34109
Clarkson, Peter A.
7
2013
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
7
2016
The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation. Zbl 0616.35080
Clarkson, Peter A.
6
1986
New integrable differential-difference systems. Zbl 0924.35157
Hu, Xing-Biao; Clarkson, Peter A.; Bullough, Robin
6
1997
Nonclassical reductions of a \((3+1)\)-cubic nonlinear Schrödinger system. Zbl 0996.35069
Mansfield, Elizabeth L.; Reid, Gregory J.; Clarkson, Peter A.
6
1998
On rational solutions of the fourth Painlevé equation and its Hamiltonian. Zbl 1091.34052
Clarkson, P. A.
6
2005
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
6
2020
Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Zbl 0931.35125
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
5
1998
Symmetry reductions of a generalized, cylindrical nonlinear Schrödinger equation. Zbl 0772.35065
Clarkson, Peter A.; Hood, Simon
5
1993
Darboux transformations and the symmetric fourth Painlevé equation. Zbl 1102.34071
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
5
2005
Symmetries and exact solutions for a \(2+1\)-dimensional shallow water wave equation. Zbl 0869.68060
Mansfield, Elizabeth L.; Clarkson, Peter A.
5
1997
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
5
2006
Hierarchies of difference equations and Bäcklund transformations. Zbl 1362.39006
Clarkson, Peter A.; Hone, Andrew N. W.; Joshi, Nalini
5
2003
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.
4
1997
The symmetry reductions of a turbulence model. Zbl 1002.35009
Bruzón, M. S.; Clarkson, P. A.; Gandarias, M. L.; Medina, E.
4
2001
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
4
1999
On integrable Ermakov-Painlevé IV systems. Zbl 1393.34083
Rogers, Colin; Bassom, Andrew P.; Clarkson, Peter A.
4
2018
Ermakov-Painlevé II reduction in cold plasma physics. Application of a Bäcklund transformation. Zbl 1411.37061
Rogers, Colin; Clarkson, Peter A.
4
2018
Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests. Zbl 0591.35061
Clarkson, Peter A.
3
1985
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
3
1999
Rational solutions and Bäcklund transformations for the third Painlevé equation. Zbl 0794.34001
Milne, A. E.; Clarkson, P. A.
3
1993
Symmetry reductions and exact solutions for a generalised Boussinesq equation. Zbl 0793.35076
Ludlow, D. K.; Clarkson, P. A.
3
1993
Integral equations and connection formulae for the Painlevé equations. Zbl 0856.34009
Clarkson, P. A.; McLeod, J. B.
3
1992
New exact solutions of the discrete fourth Painlevé equation. Zbl 0941.39502
Bassom, Andrew P.; Clarkson, Peter A.
3
1994
On the Lax pairs of the symmetric Painlevé equations. Zbl 1145.34380
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
3
2006
Asymptotics of the second Painlevé equation. Zbl 1185.33027
Clarkson, Peter A.
3
2008
Application of the isomonodromy deformation method to the fourth Painlevé equation. Zbl 0872.35108
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
3
1997
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
3
2017
Rational solutions of an extended Lotka-Volterra equation. Zbl 1362.34099
Hu, X. B.; Clarkson, P. A.
3
2002
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
3
2017
Hierarchies of exact solutions for the discrete third Painlevé equation. Zbl 1115.34302
Clarkson, Peter A.; Webster, Helen N.
2
2000
Rational solutions of the Boussinesq equation. Zbl 1173.33315
Clarkson, Peter A.
2
2008
Symmetry reductions and exact solutions of the Davey-Stewartson system. Zbl 0793.35100
Hood, S.; Clarkson, P. A.
2
1993
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.
2
1996
Shallow water wave systems. Zbl 1020.35083
Clarkson, Peter A.; Priestley, Thomas J.
2
1998
Special polynomials associated with rational and algebraic solutions of the Painlevé equations. Zbl 1165.34057
Clarkson, Peter A.
2
2006
Rational solutions of the classical Boussinesq system. Zbl 1179.35282
Clarkson, Peter A.
2
2009
Open problems for Painlevé equations. Zbl 1416.33028
Clarkson, Peter A.
2
2019
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems. Zbl 1441.81084
Clarkson, Peter A.; Gómez-Ullate, David; Grandati, Yves; Milson, Robert
6
2020
Open problems for Painlevé equations. Zbl 1416.33028
Clarkson, Peter A.
2
2019
Properties of generalized Freud polynomials. Zbl 1437.33011
Clarkson, Peter A.; Jordaan, Kerstin
11
2018
On integrable Ermakov-Painlevé IV systems. Zbl 1393.34083
Rogers, Colin; Bassom, Andrew P.; Clarkson, Peter A.
4
2018
Ermakov-Painlevé II reduction in cold plasma physics. Application of a Bäcklund transformation. Zbl 1411.37061
Rogers, Colin; Clarkson, Peter A.
4
2018
Rational solutions of the Boussinesq equation and applications to rogue waves. Zbl 1403.37073
Clarkson, Peter A.; Dowie, Ellen
17
2017
Conservation laws and integral relations for the Boussinesq equation. Zbl 1374.35301
Ankiewicz, A.; Bassom, A. P.; Clarkson, P. A.; Dowie, E.
3
2017
Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system. Zbl 1380.37133
Rogers, Colin; Clarkson, Peter A.
3
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.
1
2017
A generalized Freud weight. Zbl 1336.33022
Clarkson, Peter A.; Jordaan, Kerstin; Kelil, Abey
13
2016
On Airy solutions of the second Painlevé equation. Zbl 1346.35179
Clarkson, Peter A.
9
2016
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
7
2016
The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation. Zbl 1321.34115
Clarkson, Peter A.; Jordaan, Kerstin
18
2014
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Zbl 1275.34109
Clarkson, Peter A.
7
2013
Rogue waves, rational solutions, the patterns of their zeros and integral relations. Zbl 1189.35300
Ankiewicz, Adrian; Clarkson, Peter A.; Akhmediev, Nail
22
2010
Vortices and polynomials. Zbl 1372.37110
Clarkson, P. A.
24
2009
Rational solutions of the classical Boussinesq system. Zbl 1179.35282
Clarkson, Peter A.
2
2009
The symmetric fourth Painlevé hierarchy and associated special polynomials. Zbl 1202.34155
Filipuk, Galina V.; Clarkson, Peter A.
8
2008
Asymptotics of the second Painlevé equation. Zbl 1185.33027
Clarkson, Peter A.
3
2008
Rational solutions of the Boussinesq equation. Zbl 1173.33315
Clarkson, Peter A.
2
2008
Painlevé equations – nonlinear special functions. Zbl 1100.33006
Clarkson, Peter A.
31
2006
Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations. Zbl 1112.33015
Clarkson, Peter A.
13
2006
Symmetry group analysis of the shallow water and semi-geostrophic equations. Zbl 1088.76059
Bîlă, Nicoleta; Mansfield, Elizabeth L.; Clarkson, Peter A.
11
2006
The Lax pair for the mKdV hierarchy. Zbl 1132.37320
Clarkson, Peter A.; Joshi, Nalini; Mazzocco, Marta
7
2006
Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation. Zbl 1126.35062
Clarkson, Peter A.
7
2006
Painlevé analysis and similarity reductions for the magma equation. Zbl 1132.35328
Harris, Shirley E.; Clarkson, Peter A.
5
2006
On the Lax pairs of the symmetric Painlevé equations. Zbl 1145.34380
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
3
2006
Special polynomials associated with rational and algebraic solutions of the Painlevé equations. Zbl 1165.34057
Clarkson, Peter A.
2
2006
Special polynomials associated with rational solutions of the fifth Painlevé equation. Zbl 1077.33035
Clarkson, Peter A.
10
2005
On rational solutions of the fourth Painlevé equation and its Hamiltonian. Zbl 1091.34052
Clarkson, P. A.
6
2005
Darboux transformations and the symmetric fourth Painlevé equation. Zbl 1102.34071
Sen, A.; Hone, A. N. W.; Clarkson, P. A.
5
2005
Painlevé equations – nonlinear special functions. Zbl 1035.34101
Clarkson, Peter A.
26
2003
The second Painlevé equation, its hierarchy and associated special polynomials. Zbl 1040.33015
Clarkson, Peter A.; Mansfield, Elizabeth L.
24
2003
The fourth Painlevé equation and associated special polynomials. Zbl 1063.33029
Clarkson, Peter A.
19
2003
Remarks on the Yablonskii-Vorob’ev polynomials. Zbl 1053.34082
Clarkson, Peter A.
16
2003
The thrid Painlevé equation and associated special polynomials. Zbl 1046.33015
Clarkson, Peter A.
11
2003
Hierarchies of difference equations and Bäcklund transformations. Zbl 1362.39006
Clarkson, Peter A.; Hone, Andrew N. W.; Joshi, Nalini
5
2003
Rational solutions of an extended Lotka-Volterra equation. Zbl 1362.34099
Hu, X. B.; Clarkson, P. A.
3
2002
Symmetry, the Chazy equation and Chazy hierarchies. Zbl 1011.34078
Clarkson, Peter A.; Cosgrove, Christopher M.
1
2002
Open problems in symmetry analysis. Zbl 1172.35306
Clarkson, Peter A.; Mansfield, Elizabeth L.
7
2001
The symmetry reductions of a turbulence model. Zbl 1002.35009
Bruzón, M. S.; Clarkson, P. A.; Gandarias, M. L.; Medina, E.
4
2001
New similarity solutions of the unsteady incompressible boundary-layer equations. Zbl 1003.76019
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
10
2000
Hierarchies of exact solutions for the discrete third Painlevé equation. Zbl 1115.34302
Clarkson, Peter A.; Webster, Helen N.
2
2000
On the relation between the continuous and discrete Painlevé equations. Zbl 0994.34077
Klarkson, P. A.; Mansfield, E. L.; Webster, H. N.
1
2000
Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach. Zbl 0923.35170
Clarkson, Peter A.; Joshi, Nalini; Pickering, Andrew
35
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.
11
1999
Solitons and symmetries. Zbl 0932.35174
Ablowitz, M. J.; Clarkson, P. A.
9
1999
Symmetries of a class of nonlinear fourth order partial differential equations. Zbl 0945.35077
Clarkson, Peter A.; Priestley, Thomas J.
4
1999
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
3
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.; Nijhoff, Frank W.
1
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
18
1998
Nonclassical reductions of a \((3+1)\)-cubic nonlinear Schrödinger system. Zbl 0996.35069
Mansfield, Elizabeth L.; Reid, Gregory J.; Clarkson, Peter A.
6
1998
Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Zbl 0931.35125
Ludlow, David K.; Clarkson, Peter A.; Bassom, Andrew P.
5
1998
Shallow water wave systems. Zbl 1020.35083
Clarkson, Peter A.; Priestley, Thomas J.
2
1998
Bäcklund transformations and nonlinear superposition formulae of a differential-difference KdV equation. Zbl 0947.37051
Hu, Xingbao; Clarkson, Peter A.
1
1998
Multicomponent equations associated to non-isospectral scattering problems. Zbl 0889.35094
Clarkson, Peter A.; Gordoa, Pilar R.; Pickering, Andrew
23
1997
Bäcklund transformations and solution hierarchies for the third Painlevé equation. Zbl 0878.34006
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
18
1997
Symmetries of a class of nonlinear third-order partial differential equations. Zbl 0879.35005
Clarkson, P. A.; Mansfield, E. L.; Priestley, T. J.
12
1997
New integrable differential-difference systems. Zbl 0924.35157
Hu, Xing-Biao; Clarkson, Peter A.; Bullough, Robin
6
1997
Symmetries and exact solutions for a \(2+1\)-dimensional shallow water wave equation. Zbl 0869.68060
Mansfield, Elizabeth L.; Clarkson, Peter A.
5
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.
4
1997
Application of the isomonodromy deformation method to the fourth Painlevé equation. Zbl 0872.35108
Milne, Alice E.; Clarkson, Peter A.; Bassom, Andrew P.
3
1997
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
37
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.
19
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.
2
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.
32
1995
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 1080.35530
Clarkson, Peter A.
31
1995
Symmetry reductions and exact solutions of shallow water wave equations. Zbl 0835.35006
Clarkson, Peter A.; Mansfield, Elizabeth L.
18
1995
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation. Zbl 0846.34006
Bassom, Andrew P.; Clarkson, Peter A.; Hicks, Andrew C.
18
1995
Nonclassical symmetry reductions of the Boussinesq equation. Zbl 0952.37019
Clarkson, Peter A.
15
1995
Symmetry reductions and exact solutions of a class of nonlinear heat equations. Zbl 0812.35017
Clarkson, Peter A.; Mansfield, Elizabeth L.
80
1994
Algorithms for the nonclassical method of symmetric reductions. Zbl 0823.58036
Clarkson, Peter A.; Mansfield, Elizabeth L.
40
1994
On a shallow water wave equation. Zbl 0803.35111
Clarkson, Peter A.; Mansfield, Elizabeth L.
37
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
10
1994
Symmetry reductions, exact solutions, and Painlevé analysis for a generalized Boussinesq equation. Zbl 0810.35083
Clarkson, Peter A.; Ludlow, David K.
10
1994
New exact solutions of the discrete fourth Painlevé equation. Zbl 0941.39502
Bassom, Andrew P.; Clarkson, Peter A.
3
1994
Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations. Zbl 0788.35067
Clarkson, P. A.; Mansfield, E. L.
22
1993
Nonclassical symmetry reductions of nonlinear partial differential equations. Zbl 0805.35092
Clarkson, P. A.
11
1993
Numerical studies of the fourth Painlevé equation. Zbl 0782.65099
Bassom, A. P.; Clarkson, P. A.; Hicks, A. C.
9
1993
Symmetry reductions of a generalized, cylindrical nonlinear Schrödinger equation. Zbl 0772.35065
Clarkson, Peter A.; Hood, Simon
5
1993
Rational solutions and Bäcklund transformations for the third Painlevé equation. Zbl 0794.34001
Milne, A. E.; Clarkson, P. A.
3
1993
Symmetry reductions and exact solutions for a generalised Boussinesq equation. Zbl 0793.35076
Ludlow, D. K.; Clarkson, P. A.
3
1993
Symmetry reductions and exact solutions of the Davey-Stewartson system. Zbl 0793.35100
Hood, S.; Clarkson, P. A.
2
1993
A study of the fourth Painlevé equation. Zbl 0793.35099
Hicks, A. C.; Clarkson, P. A.; Bassom, A. P.
1
1993
Symmetries of the nonlinear heat equation. Zbl 0805.35049
Clarkson, Peter A.; Mansfield, Elizabeth L.
1
1993
The Painlevé-Kowalevski and poly-Painlevé tests for integrability. Zbl 0803.35128
Kruskal, Martin D.; Clarkson, Peter A.
29
1992
Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation. Zbl 0752.35064
Clarkson, Peter A.
21
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.
14
1992
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya- Khokhlov equation. Zbl 0771.35053
Clarkson, Peter A.; Hood, Simon
9
1992
Integral equations and connection formulae for the Painlevé equations. Zbl 0856.34009
Clarkson, P. A.; McLeod, J. B.
3
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.
30
1991
New exact solutions of the Boussinesq equation. Zbl 0721.35074
Clarkson, Peter A.
29
1990
Reductions of self-dual Yang-Mills fields and classical systems. Zbl 1050.81587
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
29
1990
Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 0719.35083
Clarkson, Peter A.
24
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.
23
1990
New similarity reductions of the Boussinesq equation. Zbl 0698.35137
Clarkson, Peter A.; Kruskal, Martin D.
271
1989
New similarity solutions for the modified Boussinesq equation. Zbl 0704.35116
Clarkson, Peter A.
29
1989
Hodograph transformations of linearizable partial differential equations. Zbl 0694.35005
Clarkson, P. A.; Fokas, A. S.; Ablowitz, M. J.
26
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.
25
1989
...and 7 more Documents
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Cited by 2,538 Authors

91 Zhang, Hongqing
62 Ma, Wen-Xiu
54 Yan, Zhenya
51 Tian, Bo
44 Tian, Shoufu
41 Chen, Yong
38 Kudryashov, Nikolaĭ Alekseevich
37 Clarkson, Peter A.
37 Gao, Yitian
35 Wazwaz, Abdul-Majid Abdul-Rahman
34 Zhang, Sheng
31 Zhang, Tiantian
26 Xia, Tie-Cheng
25 Fan, Engui
25 Lou, Senyue
25 Lü, Xing
23 Dai, Zhengde
23 Li, Biao
22 Qu, Changzheng
21 Khalique, Chaudry Masood
20 Gandarias Núñez, Maria Luz
20 He, Jingsong
20 Li, Jibin
20 Wang, Qi
19 Bekir, Ahmet
19 Liu, Hanze
19 Wen, Xiaoyong
19 Yu, Fajun
18 Wang, Xiubin
18 Zhang, Haiqiang
17 Ablowitz, Mark Jay
16 Chen, Dengyuan
16 Estévez, Pilar G.
16 Rogers, Colin
16 Song, Lina
15 Bruzón, Maria Santos
15 Filipuk, Galina V.
15 Zayed, Elsayed M. E.
14 Liu, Wenjun J.
14 Winternitz, Pavel
14 Yu, Xin
13 Shen, Shoufeng
13 Xu, Guiqiong
13 Zhang, Yufeng
12 Broadbridge, Philip
12 Geng, Xianguo
12 Grundland, Alfred Michel
12 Huang, Dingjiang
12 Inc, Mustafa
12 Meng, Xianghua
12 Popovych, Roman O.
11 Hu, Xingbiao
11 Ma, Zhengyi
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 Guha, Partha
10 Li, Zitian
10 Mihalache, Dumitru
10 Tang, Shengqiang
10 Wang, Dengshan
10 Xin, Xiangpeng
10 Yomba, Emmanuel
9 Gordoa, Pilar Ruiz
9 Liu, Xiqiang
9 Maccari, Attilio
9 Mei, Jianqin
9 Shang, Yadong
9 Sun, Zhiyuan
9 Wang, Lei
9 Xu, Tao
9 Zhang, Weiguo
9 Zhaqilao, Z.
8 Bai, Chenglin
8 Conte, Robert M.
8 Dai, Chaoqing
8 Demina, Maria V.
8 Fokas, Athanassios S.
8 Hereman, Willy A.
8 Jiang, Yan
8 Joshi, Nalini
8 Kevrekidis, Panayotis G.
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 Seadawy, Aly R.
8 Sun, Wen-Rong
8 Sun, Yepeng
8 Tian, Lixin
8 Xie, Fuding
8 Yong, Xuelin
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Cited in 279 Serials

275 Applied Mathematics and Computation
212 Chaos, Solitons and Fractals
177 Physics Letters. A
152 Journal of Mathematical Physics
107 Communications in Nonlinear Science and Numerical Simulation
94 Nonlinear Dynamics
90 Computers & Mathematics with Applications
88 Journal of Mathematical Analysis and Applications
80 Applied Mathematics Letters
63 Physica D
52 Journal of Nonlinear Mathematical Physics
46 Theoretical and Mathematical Physics
44 Studies in Applied Mathematics
39 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
29 Abstract and Applied Analysis
27 International Journal of Modern Physics B
27 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
24 Journal of Geometry and Physics
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23 Acta Applicandae Mathematicae
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19 Wave Motion
19 Mathematical Problems in Engineering
18 Mathematical and Computer Modelling
17 International Journal of Theoretical Physics
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17 Nonlinear Analysis. Real World Applications
17 Advances in Difference Equations
16 Communications in Theoretical Physics
15 Mathematics and Computers in Simulation
14 Applied Mathematics and Mechanics. (English Edition)
14 Regular and Chaotic Dynamics
13 Letters in Mathematical Physics
13 Nonlinearity
13 Chaos
12 Computer Physics Communications
12 Mathematical Methods in the Applied Sciences
12 Journal of Applied Mathematics
11 Physica A
11 ZAMP. Zeitschrift für angewandte Mathematik und Physik
11 Annals of Physics
11 Journal of Nonlinear Science
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 Nuclear Physics. B
9 Journal of Symbolic Computation
9 Numerical Methods for Partial Differential Equations
9 International Journal of Applied and Computational Mathematics
8 European Journal of Applied Mathematics
8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 Symmetry
7 Applied Mathematical Modelling
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 Constructive Approximation
6 Journal of Difference Equations and Applications
6 Discrete and Continuous Dynamical Systems
6 International Journal of Nonlinear Sciences and Numerical Simulation
6 Physical Review Letters
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5 Modern Physics Letters A
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5 SIAM Journal on Mathematical Analysis
5 Bulletin of the American Mathematical Society. New Series
5 Applied Mathematics. Series B (English Edition)
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 Physics Letters. B
4 Ukrainian Mathematical Journal
4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
4 Science in China. Series A
4 Numerical Algorithms
4 Computational Mathematics and Mathematical Physics
4 Journal of Mathematical Sciences (New York)
4 Integral Transforms and Special Functions
4 Journal of High Energy Physics
4 Journal of Applied Mathematics and Computing
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Cited in 54 Fields

2,073 Partial differential equations (35-XX)
925 Dynamical systems and ergodic theory (37-XX)
317 Ordinary differential equations (34-XX)
271 Fluid mechanics (76-XX)
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160 Quantum theory (81-XX)
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66 Statistical mechanics, structure of matter (82-XX)
56 Optics, electromagnetic theory (78-XX)
55 Mechanics of deformable solids (74-XX)
54 Difference and functional equations (39-XX)
44 Mechanics of particles and systems (70-XX)
39 Differential geometry (53-XX)
37 Operator theory (47-XX)
33 Functions of a complex variable (30-XX)
31 Relativity and gravitational theory (83-XX)
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