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## Gibbon, John D.

Compute Distance To:
 Author ID: gibbon.john-d Published as: Gibbon, J.; Gibbon, J. D.; Gibbon, John; Gibbon, John D. External Links: MGP
 Documents Indexed: 94 Publications since 1965, including 3 Books
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#### Co-Authors

 22 single-authored 16 Doering, Charles R. 11 Holm, Darryl D. 6 Bartuccelli, Michele V. 5 Kerr, Robert M. 5 McGuinness, Mark J. 4 Dodd, Roger K. 4 Gupta, Anupam 4 Ohkitani, Koji 3 Heritage, M. 3 Malham, Simon J. A. 3 Pandit, Rahul 3 Roulstone, Ian 3 Tabor, Michael 3 Titi, Edriss Saleh 3 Vincenzi, Dario 2 Banos, Bertrand 2 Caudrey, P. J. 2 Constantin, Peter 2 Donzis, Diego A. 2 Eilbeck, John Chris 2 Fowler, Andrew C. 2 Galanti, Barak 2 James, I. N. 2 Moroz, Irene M. 2 Nicolaenko, Basil 2 Rao, Pooja 2 Rubtsov, Vladimir Nikolaevich 1 Atiyah, Michael Francis 1 Bartucelli, M. V. 1 Berkshire, Frank H. 1 Bullough, Robin K. 1 Bustamante, Miguel D. 1 Caulfield, C. P. 1 Caulfield, Colm-Cille P. 1 Christiansen, Peter Leth 1 Doering, C. D. 1 Elgin, John N. 1 Eshraghi, Hossein 1 Foiaş, Ciprian Ilie 1 Fokas, Athanassios S. 1 Gibbons, John 1 Gisselfält, Magnus 1 If, F. 1 Levermore, C. David 1 McGill, William J. 1 Moore, Daniel R. 1 Morris, Hedley C. 1 Newell, Alan C. 1 Oliver, Marcel 1 Pal, Nairita 1 Pavliotis, Greg A. 1 Plan, Emmanuel Lance Christopher VI Medillo 1 Radmore, Paul M. 1 Skovgaard, Ove 1 Stuart, J. T. 1 Tabors, M. 1 Thiffeault, Jean-Luc 1 Wilson, G. Jeyaraj 1 Wood, David Harlan 1 Zeng, Yunbo
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#### Serials

 17 Nonlinearity 16 Physica D 6 Journal of Fluid Mechanics 5 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 4 Journal of Mathematical Physics 4 Journal of Mathematical Psychology 3 Physics of Fluids 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Studies in Applied Mathematics 2 Journal of Nonlinear Science 2 Journal of Physics A: Mathematical and Theoretical 1 Archive for Rational Mechanics and Analysis 1 IMA Journal of Applied Mathematics 1 Physics Letters. A 1 Russian Mathematical Surveys 1 Indiana University Mathematics Journal 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Dynamics and Stability of Systems 1 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences 1 RIMS Kokyuroku 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Physica Scripta 1 Communications in Mathematical Sciences 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Cambridge Texts in Applied Mathematics
all top 5

#### Fields

 68 Partial differential equations (35-XX) 68 Fluid mechanics (76-XX) 13 Dynamical systems and ergodic theory (37-XX) 5 Geophysics (86-XX) 4 Probability theory and stochastic processes (60-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Ordinary differential equations (34-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

75 Publications have been cited 1,587 times in 1,252 Documents Cited by Year
Solitons and nonlinear wave equations. Zbl 0496.35001
Dodd, R. K.; Eilbeck, J. C.; Gibbon, J. D.; Morris, H. C.
1982
Applied analysis of the Navier-Stokes equations. Zbl 0838.76016
Doering, Charles R.; Gibbon, J. D.
1995
A new hierarchy of Korteweg-de Vries equations. Zbl 0346.35024
Caudrey, P. J.; Dodd, R. K.; Gibbon, J. D.
1976
Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021
Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil
1988
Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119
Doering, Charles R.; Gibbon, John D.; Levermore, C. David
1994
The complex Lorenz equations. Zbl 1194.37039
Fowler, A. C.; Gibbon, J. D.; McGuinness, M. J.
1982
On the possibility of soft and hard turbulence in the complex Ginzburg- Landau equation. Zbl 0702.76061
Bartuccelli, Michele; Constantin, Petre; Doering, Charles R.; Gibbon, John D.; Gisselfält, Magnus
1990
The real and complex Lorenz equations in rotating fluids and lasers. Zbl 1194.76280
Gibbon, J. D.; Mcguinness, M. J.
1982
The three-dimensional Euler equations: Where do we stand? Zbl 1143.76389
Gibbon, J. D.
2008
The real and complex Lorenz equations and their relevance to physical systems. Zbl 1194.76087
Fowler, A. C.; Gibbon, J. D.; Mcguinness, M. J.
1983
The general-gamma distribution and reaction times. Zbl 0134.37902
McGill, W. J.; Gibbon, J.
1965
The prolongation structure of a higher order Korteweg-de Vries equation. Zbl 0376.35009
Dodd, R. K.; Gibbon, J. D.
1978
Length scales in solutions of the complex Ginzburg-Landau equation. Zbl 0885.35012
Bartuccelli, Michele V.; Gibbon, John D.; Oliver, Marcel
1996
The Painlevé property and Hirota’s method. Zbl 0581.35074
Gibbon, J. D.; Radmore, P.; Tabor, M.; Wood, David Harlan
1985
A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184
Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D.
2004
Numerical study of singularity formation in a class of Euler and Navier-Stokes flows. Zbl 1184.76402
Ohkitani, Koji; Gibbon, John D.
2000
Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations. Zbl 0956.76018
Gibbon, J. D.; Fokas, A. S.; Doering, C. R.
1999
An example of soliton behaviour in a rotating baroclinic fluid. Zbl 0423.76016
Gibbon, J. D.; James, I. N.; Moroz, I. M.
1979
Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations. Zbl 0912.76020
Galanti, B.; Gibbon, J. D.; Heritage, M.
1997
A quaternionic structure in the three-dimensional Euler and ideal magneto-hydrodynamics equations. Zbl 1011.35110
Gibbon, J. D.
2002
Quaternions and particle dynamics in the Euler fluid equations. Zbl 1145.76012
Gibbon, J. D.; Holm, D. D.; Kerr, R. M.; Roulstone, I.
2006
On the shape and dimension of the Lorenz attractor. Zbl 0838.34070
Doering, Charles R.; Gibbon, J. D.
1995
Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations. Zbl 1040.35069
Gibbon, J. D.; Moore, D. R.; Stuart, J. T.
2003
Length scales in solutions of the Navier-Stokes equations. Zbl 0782.35056
Bartucelli, M. V.; Doering, C. R.; Gibbon, J. D.; Malham, S. J. A.
1993
Lax pairs, Bäcklund transformations and special solutions for ordinary differential equations. Zbl 0682.34011
Gibbon, J. D.; Newell, A. C.; Tabors, M.; Zeng, Y. B.
1988
Amplitude equations at the critical points of unstable dispersive physical systems. Zbl 0476.35054
Gibbon, J. D.; McGuinness, M. J.
1981
Estimates for the LANS-$$\alpha$$, Leray-$$\alpha$$ and Bardina models in terms of a Navier-Stokes Reynolds number. Zbl 1157.76009
Gibbon, J. D.; Holm, D. D.
2008
The three-dimensional Euler equations: singular or non-singular? Zbl 1160.35498
Gibbon, J. D.; Bustamante, M.; Kerr, R. M.
2008
The sine-Gordon equation as a model for a rapidly rotating baroclinic fluid. Zbl 1063.76534
Gibbon, J. D.; James, I. N.; Moroz, I. M.
1979
Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 0997.35046
Doering, Charles R.; Gibbon, J. D.
2002
Attractor dimension and small length scale estimates for the three-dimensional Navier-Stokes equations. Zbl 0906.35069
Gibbon, J. D.; Titi, E. S.
1997
Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030
Doering, Charles R.; Gibbon, John D.
1991
Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations. Zbl 1294.76159
Donzis, Diego A.; Gibbon, John D.; Gupta, Anupam; Kerr, Robert M.; Pandit, Rahul; Vincenzi, Dario
2013
Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality. Zbl 1272.46020
Bartuccelli, Michele V.; Gibbon, John D.
2011
Intermittency and regularity issues in $$3D$$ Navier-Stokes turbulence. Zbl 1129.76014
Gibbon, J. D.; Doering, Charles R.
2005
Singularity formation in a class of stretched solutions of the equations for ideal magneto-hydrodynamics. Zbl 1016.76097
Gibbon, J. D.; Ohkitani, K.
2001
Regularity and singularity in solutions of the three-dimensional Navier-Stokes equations. Zbl 1211.76030
Gibbon, J. D.
2010
Length-scale estimates for the LANS-$$\alpha$$ equations in terms of the Reynolds number. Zbl 1331.76051
Gibbon, J. D.; Holm, D. D.
2006
A survey of the origins and physical importance of soliton equations. Zbl 0579.35076
Gibbon, J. D.
1985
Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations. Zbl 1298.76059
Gibbon, John D.; Donzis, Diego A.; Gupta, Anupam; Kerr, Robert M.; Pandit, Rahul; Vincenzi, Dario
2014
The 3D incompressible Euler equations with a passive scalar: a road to blow-up? Zbl 1292.35216
Gibbon, John D.; Titi, Edriss S.
2013
The dynamics of the gradient of potential vorticity. Zbl 1278.76017
Gibbon, J. D.; Holm, D. D.
2010
Cluster formation in complex multi-scale systems. Zbl 1206.82123
Gibbon, J. D.; Titi, E. S.
2005
Aspects of the Painlevé property for partial differential equations. Zbl 0608.35069
Tabor, M.; Gibbon, J. D.
1986
Conditional regularity of solutions of the three-dimensional Navier-Stokes equations and implications for intermittency. Zbl 1452.76047
Gibbon, J. D.
2012
A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1291.35181
Gibbon, J. D.
2012
A geometric interpretation of coherent structures in Navier-Stokes flows. Zbl 1186.76638
Roulstone, I.; Banos, B.; Gibbon, J. D.; Roubtsov, V. N.
2009
Lagrangian particle paths and ortho-normal quaternion frames. Zbl 1118.76017
Gibbon, J. D.; Holm, D. D.
2007
Intermittency in solutions of the three-dimensional Navier-Stokes equations. Zbl 1034.76013
Gibbon, J. D.; Doering, Charles R.
2003
The prolongation structures of a class of nonlinear evolution equations. Zbl 0384.35051
Dodd, R. K.; Gibbon, J. D.
1978
The role of BKM-type theorems in $$3D$$ Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis. Zbl 1398.76033
Gibbon, John D.; Gupta, Anupam; Pal, Nairita; Pandit, Rahul
2018
Nonlinear effects in buoyancy-driven variable-density turbulence. Zbl 1383.76211
Rao, P.; Caulfield, C. P.; Gibbon, J. D.
2017
Estimating intermittency in three-dimensional Navier-Stokes turbulence. Zbl 1171.76382
Gibbon, J. D.
2009
Estimates for the two-dimensional Navier-Stokes equations in terms of the Reynolds number. Zbl 1144.81348
Gibbon, J. D.; Pavliotis, G. A.
2007
Evidence for singularity formation in a class of stretched solutions of the equations for ideal MHD. Zbl 1142.76510
Gibbon, J. D.; Ohkitani, K.
2002
Stretching and compression of vorticity in the 3D Euler equations. Zbl 0997.76014
Gibbon, J. D.; Galanti, B.; Kerr, R. M.
2000
Ladder theorems for the $$2D$$ and $$3D$$ Navier-Stokes equations on a finite periodic domain. Zbl 0736.35084
Bartuccelli, M.; Doering, C.; Gibbon, J. D.
1991
Finite-dimensional attractor for the laser equations. Zbl 0696.35101
Constantin, P.; Foias, C.; Gibbon, J. D.
1989
Finite dimensionality in the complex Ginzburg-Landau equation. Zbl 0741.35079
Doering, C. R.; Gibbon, J. D.; Holm, D. D.; Nicolaenko, B.
1989
On the one-and two-dimensional Toda lattices and the Painlevé property. Zbl 0573.70023
Gibbon, J. D.; Tabor, M.
1985
Orthonormal quaternion frames, Lagrangian evolution equations, and the three-dimensional Euler equations. Zbl 1203.76015
Gibbon, J. D.
2007
Angular dependence and growth of vorticity in the three-dimensional Euler equations. Zbl 1185.35157
Gibbon, J. D.; Heritage, M.
1997
Collapse in the $$n$$-dimensional nonlinear Schrödinger equation - a parallel with Sundman’s results in the N-body problem. Zbl 0536.35063
Berkshire, F. H.; Gibbon, J. D.
1983
On the form and location of the psychometric bisection function for time. Zbl 0475.92019
Gibbon, John
1981
Weak and strong solutions of the $$3D$$ Navier-Stokes equations and their relation to a chessboard of convergent inverse length scales. Zbl 1411.76021
Gibbon, J. D.
2019
Lyapunov dimension of elastic turbulence. Zbl 1383.76029
Plan, Emmanuel Lance Christopher VI M.; Gupta, Anupam; Vincenzi, Dario; Gibbon, John D.
2017
High-low frequency slaving and regularity issues in the 3D Navier-Stokes equations. Zbl 1338.35333
Gibbon, J. D.
2016
Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations. Zbl 1296.35130
Gibbon, John D.; Holm, Darryl D.
2012
Extreme events in solutions of hydrostatic and non-hydrostatic climate models. Zbl 1219.86004
Gibbon, J. D.; Holm, D. D.
2011
A voyage around the Navier-Stokes equations. Zbl 1031.76516
Gibbon, J. D.
1996
Length scales and ladder theorems for $$2d$$ and $$3d$$ convection. Zbl 0814.35095
Gibbon, J. D.
1995
Derivation of $$3d$$ Navier-Stokes length scales from a result of Foias, Guillopé and Temam. Zbl 0841.35080
Gibbon, J. D.
1994
Dispersive instabilities in nonlinear systems: The real and complex Lorenz equation. Zbl 0503.58035
Gibbon, J. D.
1981
N-soliton solutions of some non-linear dispersive wave equations of physical significance. Zbl 0312.35016
Gibbon, J. D.; Caudrey, P. J.; Bullough, R. K.; Eilbeck, J. C.
1974
Scalar timing and semi-Markov chains in free-operant avoidance. Zbl 0211.23401
Gibbon, J.
1971
Weak and strong solutions of the $$3D$$ Navier-Stokes equations and their relation to a chessboard of convergent inverse length scales. Zbl 1411.76021
Gibbon, J. D.
2019
The role of BKM-type theorems in $$3D$$ Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis. Zbl 1398.76033
Gibbon, John D.; Gupta, Anupam; Pal, Nairita; Pandit, Rahul
2018
Nonlinear effects in buoyancy-driven variable-density turbulence. Zbl 1383.76211
Rao, P.; Caulfield, C. P.; Gibbon, J. D.
2017
Lyapunov dimension of elastic turbulence. Zbl 1383.76029
Plan, Emmanuel Lance Christopher VI M.; Gupta, Anupam; Vincenzi, Dario; Gibbon, John D.
2017
High-low frequency slaving and regularity issues in the 3D Navier-Stokes equations. Zbl 1338.35333
Gibbon, J. D.
2016
Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations. Zbl 1298.76059
Gibbon, John D.; Donzis, Diego A.; Gupta, Anupam; Kerr, Robert M.; Pandit, Rahul; Vincenzi, Dario
2014
Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations. Zbl 1294.76159
Donzis, Diego A.; Gibbon, John D.; Gupta, Anupam; Kerr, Robert M.; Pandit, Rahul; Vincenzi, Dario
2013
The 3D incompressible Euler equations with a passive scalar: a road to blow-up? Zbl 1292.35216
Gibbon, John D.; Titi, Edriss S.
2013
Conditional regularity of solutions of the three-dimensional Navier-Stokes equations and implications for intermittency. Zbl 1452.76047
Gibbon, J. D.
2012
A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1291.35181
Gibbon, J. D.
2012
Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations. Zbl 1296.35130
Gibbon, John D.; Holm, Darryl D.
2012
Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality. Zbl 1272.46020
Bartuccelli, Michele V.; Gibbon, John D.
2011
Extreme events in solutions of hydrostatic and non-hydrostatic climate models. Zbl 1219.86004
Gibbon, J. D.; Holm, D. D.
2011
Regularity and singularity in solutions of the three-dimensional Navier-Stokes equations. Zbl 1211.76030
Gibbon, J. D.
2010
The dynamics of the gradient of potential vorticity. Zbl 1278.76017
Gibbon, J. D.; Holm, D. D.
2010
A geometric interpretation of coherent structures in Navier-Stokes flows. Zbl 1186.76638
Roulstone, I.; Banos, B.; Gibbon, J. D.; Roubtsov, V. N.
2009
Estimating intermittency in three-dimensional Navier-Stokes turbulence. Zbl 1171.76382
Gibbon, J. D.
2009
The three-dimensional Euler equations: Where do we stand? Zbl 1143.76389
Gibbon, J. D.
2008
Estimates for the LANS-$$\alpha$$, Leray-$$\alpha$$ and Bardina models in terms of a Navier-Stokes Reynolds number. Zbl 1157.76009
Gibbon, J. D.; Holm, D. D.
2008
The three-dimensional Euler equations: singular or non-singular? Zbl 1160.35498
Gibbon, J. D.; Bustamante, M.; Kerr, R. M.
2008
Lagrangian particle paths and ortho-normal quaternion frames. Zbl 1118.76017
Gibbon, J. D.; Holm, D. D.
2007
Estimates for the two-dimensional Navier-Stokes equations in terms of the Reynolds number. Zbl 1144.81348
Gibbon, J. D.; Pavliotis, G. A.
2007
Orthonormal quaternion frames, Lagrangian evolution equations, and the three-dimensional Euler equations. Zbl 1203.76015
Gibbon, J. D.
2007
Quaternions and particle dynamics in the Euler fluid equations. Zbl 1145.76012
Gibbon, J. D.; Holm, D. D.; Kerr, R. M.; Roulstone, I.
2006
Length-scale estimates for the LANS-$$\alpha$$ equations in terms of the Reynolds number. Zbl 1331.76051
Gibbon, J. D.; Holm, D. D.
2006
Intermittency and regularity issues in $$3D$$ Navier-Stokes turbulence. Zbl 1129.76014
Gibbon, J. D.; Doering, Charles R.
2005
Cluster formation in complex multi-scale systems. Zbl 1206.82123
Gibbon, J. D.; Titi, E. S.
2005
A bound on mixing efficiency for the advection-diffusion equation. Zbl 1065.76184
Thiffeault, Jean-Luc; Doering, Charles R.; Gibbon, John D.
2004
Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations. Zbl 1040.35069
Gibbon, J. D.; Moore, D. R.; Stuart, J. T.
2003
Intermittency in solutions of the three-dimensional Navier-Stokes equations. Zbl 1034.76013
Gibbon, J. D.; Doering, Charles R.
2003
A quaternionic structure in the three-dimensional Euler and ideal magneto-hydrodynamics equations. Zbl 1011.35110
Gibbon, J. D.
2002
Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations. Zbl 0997.35046
Doering, Charles R.; Gibbon, J. D.
2002
Evidence for singularity formation in a class of stretched solutions of the equations for ideal MHD. Zbl 1142.76510
Gibbon, J. D.; Ohkitani, K.
2002
Singularity formation in a class of stretched solutions of the equations for ideal magneto-hydrodynamics. Zbl 1016.76097
Gibbon, J. D.; Ohkitani, K.
2001
Numerical study of singularity formation in a class of Euler and Navier-Stokes flows. Zbl 1184.76402
Ohkitani, Koji; Gibbon, John D.
2000
Stretching and compression of vorticity in the 3D Euler equations. Zbl 0997.76014
Gibbon, J. D.; Galanti, B.; Kerr, R. M.
2000
Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations. Zbl 0956.76018
Gibbon, J. D.; Fokas, A. S.; Doering, C. R.
1999
Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations. Zbl 0912.76020
Galanti, B.; Gibbon, J. D.; Heritage, M.
1997
Attractor dimension and small length scale estimates for the three-dimensional Navier-Stokes equations. Zbl 0906.35069
Gibbon, J. D.; Titi, E. S.
1997
Angular dependence and growth of vorticity in the three-dimensional Euler equations. Zbl 1185.35157
Gibbon, J. D.; Heritage, M.
1997
Length scales in solutions of the complex Ginzburg-Landau equation. Zbl 0885.35012
Bartuccelli, Michele V.; Gibbon, John D.; Oliver, Marcel
1996
A voyage around the Navier-Stokes equations. Zbl 1031.76516
Gibbon, J. D.
1996
Applied analysis of the Navier-Stokes equations. Zbl 0838.76016
Doering, Charles R.; Gibbon, J. D.
1995
On the shape and dimension of the Lorenz attractor. Zbl 0838.34070
Doering, Charles R.; Gibbon, J. D.
1995
Length scales and ladder theorems for $$2d$$ and $$3d$$ convection. Zbl 0814.35095
Gibbon, J. D.
1995
Weak and strong solutions of the complex Ginzburg-Landau equation. Zbl 0810.35119
Doering, Charles R.; Gibbon, John D.; Levermore, C. David
1994
Derivation of $$3d$$ Navier-Stokes length scales from a result of Foias, Guillopé and Temam. Zbl 0841.35080
Gibbon, J. D.
1994
Length scales in solutions of the Navier-Stokes equations. Zbl 0782.35056
Bartucelli, M. V.; Doering, C. R.; Gibbon, J. D.; Malham, S. J. A.
1993
Note on the Constantin-Foias-Temam attractor dimension estimate for two- dimensional turbulence. Zbl 0728.76030
Doering, Charles R.; Gibbon, John D.
1991
Ladder theorems for the $$2D$$ and $$3D$$ Navier-Stokes equations on a finite periodic domain. Zbl 0736.35084
Bartuccelli, M.; Doering, C.; Gibbon, J. D.
1991
On the possibility of soft and hard turbulence in the complex Ginzburg- Landau equation. Zbl 0702.76061
Bartuccelli, Michele; Constantin, Petre; Doering, Charles R.; Gibbon, John D.; Gisselfält, Magnus
1990
Finite-dimensional attractor for the laser equations. Zbl 0696.35101
Constantin, P.; Foias, C.; Gibbon, J. D.
1989
Finite dimensionality in the complex Ginzburg-Landau equation. Zbl 0741.35079
Doering, C. R.; Gibbon, J. D.; Holm, D. D.; Nicolaenko, B.
1989
Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021
Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil
1988
Lax pairs, Bäcklund transformations and special solutions for ordinary differential equations. Zbl 0682.34011
Gibbon, J. D.; Newell, A. C.; Tabors, M.; Zeng, Y. B.
1988
Aspects of the Painlevé property for partial differential equations. Zbl 0608.35069
Tabor, M.; Gibbon, J. D.
1986
The Painlevé property and Hirota’s method. Zbl 0581.35074
Gibbon, J. D.; Radmore, P.; Tabor, M.; Wood, David Harlan
1985
A survey of the origins and physical importance of soliton equations. Zbl 0579.35076
Gibbon, J. D.
1985
On the one-and two-dimensional Toda lattices and the Painlevé property. Zbl 0573.70023
Gibbon, J. D.; Tabor, M.
1985
The real and complex Lorenz equations and their relevance to physical systems. Zbl 1194.76087
Fowler, A. C.; Gibbon, J. D.; Mcguinness, M. J.
1983
Collapse in the $$n$$-dimensional nonlinear Schrödinger equation - a parallel with Sundman’s results in the N-body problem. Zbl 0536.35063
Berkshire, F. H.; Gibbon, J. D.
1983
Solitons and nonlinear wave equations. Zbl 0496.35001
Dodd, R. K.; Eilbeck, J. C.; Gibbon, J. D.; Morris, H. C.
1982
The complex Lorenz equations. Zbl 1194.37039
Fowler, A. C.; Gibbon, J. D.; McGuinness, M. J.
1982
The real and complex Lorenz equations in rotating fluids and lasers. Zbl 1194.76280
Gibbon, J. D.; Mcguinness, M. J.
1982
Amplitude equations at the critical points of unstable dispersive physical systems. Zbl 0476.35054
Gibbon, J. D.; McGuinness, M. J.
1981
On the form and location of the psychometric bisection function for time. Zbl 0475.92019
Gibbon, John
1981
Dispersive instabilities in nonlinear systems: The real and complex Lorenz equation. Zbl 0503.58035
Gibbon, J. D.
1981
An example of soliton behaviour in a rotating baroclinic fluid. Zbl 0423.76016
Gibbon, J. D.; James, I. N.; Moroz, I. M.
1979
The sine-Gordon equation as a model for a rapidly rotating baroclinic fluid. Zbl 1063.76534
Gibbon, J. D.; James, I. N.; Moroz, I. M.
1979
The prolongation structure of a higher order Korteweg-de Vries equation. Zbl 0376.35009
Dodd, R. K.; Gibbon, J. D.
1978
The prolongation structures of a class of nonlinear evolution equations. Zbl 0384.35051
Dodd, R. K.; Gibbon, J. D.
1978
A new hierarchy of Korteweg-de Vries equations. Zbl 0346.35024
Caudrey, P. J.; Dodd, R. K.; Gibbon, J. D.
1976
N-soliton solutions of some non-linear dispersive wave equations of physical significance. Zbl 0312.35016
Gibbon, J. D.; Caudrey, P. J.; Bullough, R. K.; Eilbeck, J. C.
1974
Scalar timing and semi-Markov chains in free-operant avoidance. Zbl 0211.23401
Gibbon, J.
1971
The general-gamma distribution and reaction times. Zbl 0134.37902
McGill, W. J.; Gibbon, J.
1965
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#### Cited by 1,823 Authors

 29 Gibbon, John D. 21 Guo, Boling 18 Doering, Charles R. 18 Mahmoud, Gamal M. 17 Titi, Edriss Saleh 13 Bartuccelli, Michele V. 12 Jolly, Michael S. 12 Mahmoud, Emad E. 11 Robinson, James Cooper 11 Wu, Jiahong 10 Foiaş, Ciprian Ilie 10 Kudryashov, Nikolaĭ Alekseevich 10 Osborne, Alfred R. 8 Feng, Zhaosheng 8 Gao, Hongjun 8 Liu, Shutang 8 Pérez-García, Víctor Manuel 8 Wang, Xiaoming 8 Wu, Xinyuan 7 Clarkson, Peter A. 7 Duan, Jinqiao 7 Gao, Yitian 7 Liu, Changying 6 Geng, Xianguo 6 Helal, Mohamed Atef 6 Hou, Thomas Yizhao 6 Kerr, Robert M. 6 Lu, Shujuan 6 Mancas, Stefan C. 6 Ohkitani, Koji 6 Parker, Allen 6 Protas, Bartosz 6 Qu, Changzheng 6 Roychoudhury, Satrajit 6 Thiffeault, Jean-Luc 6 Zhou, Xiaobing 5 Aly, Shaban A. H. 5 Baccouch, Mahboub 5 Boritchev, Alexandre 5 Bu, Charles 5 Constantin, Peter 5 Dascaliuc, Radu 5 Dehghan Takht Fooladi, Mehdi 5 Doelman, Arjen 5 Fang, Tao 5 Layton, William J. 5 Leonov, Gennadiĭ Alekseevich 5 Levermore, C. David 5 Liu, Zhengrong 5 Łukaszewicz, Grzegorz 5 Oliver, Marcel 5 Salas, Alvaro H. 5 Shu, Ji 5 Sun, Ji Tao 5 Temam, Roger Meyer 5 Townsend, James T. 5 Vázquez, Luis 5 Wazwaz, Abdul-Majid Abdul-Rahman 5 Wu, Zhaoyan 5 Zhang, Fangfang 5 Zhang, Hongqing 4 Ahmed, Mansour E. 4 Belmonte-Beitia, Juan 4 Bergamasco, L. 4 Cai, Xiaomei 4 Chae, Dongho 4 Choudhury, Sumitra Roy 4 David, Claire 4 Demirkus, Dilek 4 Elgindi, Tarek Mohamed 4 Fokas, Athanassios S. 4 Fu, Xinchu 4 Fuchssteiner, Benno 4 Gordoa, Pilar Ruiz 4 Gupta, Anupam 4 Hereman, Willy A. 4 Holm, Darryl D. 4 Jagtap, Ameya D. 4 Jeffrey, Alan P. 4 Jiang, Murong 4 Kevrekidis, Panayotis G. 4 Khoshnevisan, Davar 4 Kim, Kunwoo 4 Korotyaev, Evgeny L. 4 Kukavica, Igor 4 Lewandowski, Roger 4 Liu, Jian 4 Liu, Qingping 4 Lu, Hong 4 Olson, Eric J. 4 Popov, S. P. 4 Prudhomme, Serge 4 Sagaut, Pierre 4 Schweickert, Richard 4 Twizell, E. H. 4 Wang, Baoxiang 4 Wang, Bixiang 4 Yan, Zhenya 3 Adamashvili, G. T. 3 Al-Kashif, M. A. ...and 1,723 more Authors
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#### Cited in 234 Serials

 104 Physica D 67 Journal of Mathematical Physics 59 Applied Mathematics and Computation 52 Physics Letters. A 46 Chaos, Solitons and Fractals 43 Journal of Fluid Mechanics 39 Journal of Mathematical Analysis and Applications 28 Journal of Differential Equations 27 Nonlinear Dynamics 21 Journal of Computational Physics 21 Communications in Nonlinear Science and Numerical Simulation 17 Physics of Fluids 16 Journal of Mathematical Psychology 16 Applied Mathematics Letters 16 Journal of Nonlinear Science 15 Communications in Mathematical Physics 15 Chaos 14 Wave Motion 14 Mathematical Problems in Engineering 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Applied Numerical Mathematics 13 Abstract and Applied Analysis 13 Journal of Nonlinear Mathematical Physics 12 Computers & Mathematics with Applications 12 Computer Physics Communications 12 Studies in Applied Mathematics 12 Numerical Methods for Partial Differential Equations 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Mathematics and Computers in Simulation 10 Computer Methods in Applied Mechanics and Engineering 10 Theoretical and Mathematical Physics 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Archive for Rational Mechanics and Analysis 9 Journal of Computational and Applied Mathematics 8 Journal of the Franklin Institute 8 Mathematical Methods in the Applied Sciences 8 Physica A 8 Applied Mathematics and Mechanics. (English Edition) 8 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 7 Applicable Analysis 7 Acta Applicandae Mathematicae 7 Communications in Partial Differential Equations 7 International Journal of Computer Mathematics 7 Nonlinear Analysis. Real World Applications 7 Discrete and Continuous Dynamical Systems. Series B 7 Advances in Difference Equations 6 Reports on Mathematical Physics 6 Numerical Functional Analysis and Optimization 6 Applied Mathematical Modelling 6 Journal of Mathematical Fluid Mechanics 6 Journal of Applied Mathematics 5 Communications on Pure and Applied Mathematics 5 International Journal of Engineering Science 5 Nonlinearity 5 Psychometrika 5 Journal of Functional Analysis 5 Computational Mathematics and Mathematical Physics 5 Journal of Dynamics and Differential Equations 5 Journal of Mathematical Sciences (New York) 5 Complexity 5 Discrete and Continuous Dynamical Systems 5 European Journal of Mechanics. B. Fluids 4 Journal of Engineering Mathematics 4 Journal of Statistical Physics 4 Letters in Mathematical Physics 4 Journal of Geometry and Physics 4 Chinese Annals of Mathematics. Series B 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Acta Mathematicae Applicatae Sinica. English Series 4 Mathematical and Computer Modelling 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Applied Mathematics 4 Regular and Chaotic Dynamics 4 Acta Mathematica Sinica. English Series 4 Nonlinear Analysis. Theory, Methods & Applications 3 International Journal for Numerical Methods in Fluids 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Journal of Scientific Computing 3 Applications of Mathematics 3 Numerical Algorithms 3 Journal of Vibration and Control 3 Qualitative Theory of Dynamical Systems 3 International Journal of Modern Physics C 3 Physical Review Letters 3 Differential Equations 3 Analysis and Applications (Singapore) 3 Advances in Mathematical Physics 3 Journal of Applied Analysis and Computation 2 Modern Physics Letters A 2 International Journal of Modern Physics B 2 Computers and Fluids 2 Geophysical and Astrophysical Fluid Dynamics 2 International Journal of Theoretical Physics 2 Physics of Fluids 2 Physics Reports 2 Mathematics of Computation 2 Prikladnaya Matematika i Mekhanika 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Probability 2 Automatica ...and 134 more Serials
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#### Cited in 48 Fields

 827 Partial differential equations (35-XX) 375 Fluid mechanics (76-XX) 314 Dynamical systems and ergodic theory (37-XX) 198 Numerical analysis (65-XX) 142 Ordinary differential equations (34-XX) 56 Systems theory; control (93-XX) 52 Quantum theory (81-XX) 51 Statistical mechanics, structure of matter (82-XX) 45 Probability theory and stochastic processes (60-XX) 31 Mechanics of deformable solids (74-XX) 27 Geophysics (86-XX) 24 Global analysis, analysis on manifolds (58-XX) 22 Mechanics of particles and systems (70-XX) 18 Statistics (62-XX) 17 Computer science (68-XX) 17 Classical thermodynamics, heat transfer (80-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Operator theory (47-XX) 16 Optics, electromagnetic theory (78-XX) 14 Biology and other natural sciences (92-XX) 11 Special functions (33-XX) 9 Differential geometry (53-XX) 8 Information and communication theory, circuits (94-XX) 7 Functional analysis (46-XX) 7 Operations research, mathematical programming (90-XX) 6 Topological groups, Lie groups (22-XX) 6 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 5 Approximations and expansions (41-XX) 4 Algebraic geometry (14-XX) 4 Measure and integration (28-XX) 4 Difference and functional equations (39-XX) 4 Integral equations (45-XX) 3 Nonassociative rings and algebras (17-XX) 3 Group theory and generalizations (20-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 Relativity and gravitational theory (83-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Astronomy and astrophysics (85-XX)