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Grimshaw, Roger Hamilton James

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Author ID: grimshaw.roger-h-j Recent zbMATH articles by "Grimshaw, Roger Hamilton James"
Published as: Grimshaw, R.; Grimshaw, R. H.; Grimshaw, R. H. J.; Grimshaw, R. J. H.; Grimshaw, Roger; Grimshaw, Roger H.; Grimshaw, Roger H. J.
External Links: MGP · Math-Net.Ru · ResearchGate · dblp
Documents Indexed: 245 Publications since 1964, including 3 Books
Biographic References: 2 Publications
all top 5

Co-Authors

67 single-authored
14 Pelinovsky, Efim
13 Malomed, Boris A.
12 El, Gennady A.
11 Pelinovsky, Dmitry Efimovich
9 Chow, Kwok Wing
9 Clarke, Simon R.
8 Maleewong, Montri
8 Talipova, Tatiana
7 Johnson, Edward Robert
7 Khusnutdinova, Karima Robertovna
6 Pullin, Dale I.
6 Tian, Xin
5 Derzho, Oleg G.
5 Hooper, Alison P.
5 Smyth, Noel F.
5 Stepanyants, Yury A.
4 Helfrich, Karl R.
4 Kamchatnov, Anatoly M.
4 Ostrovsky, Lev A.
4 Yuan, Chunxin
3 Akylas, T. R.
3 Asavanant, Jack
3 Benilov, Eugene S.
3 Broutman, Dave
3 Caillol, Philippe
3 Christodoulides, Paul
3 Gottwald, Georg A.
3 He, Jianming
3 Liu, Zihua
3 Mu, Gui
3 Qin, Zhenyun
3 Reznik, Gregory M.
3 Yi, Zengxin
2 Aigner, Andreas A.
2 Alias, Azwani
2 Allen, John S.
2 Barnes, Belinda
2 Chan, Hiu Ning
2 Collings, I. L.
2 Denier, James P.
2 Dias, Frédéric
2 Ee, Bernard K.
2 Gear, John Anthony
2 Gil’man, O. A.
2 Griffiths, Stephen D.
2 Lee, Seungjoon
2 Mitsudera, Humio
2 Myint, S.
2 Pavlov, Maxim V.
2 Pelinovsky, E. N.
2 Pudjaprasetya, Sri Redjeki
2 Slunyaev, Alexey V.
2 Zhu, Yong
1 Akhmediev, Nail N.
1 Annenkov, Sergei Yu.
1 Antanovskii, Leonid K.
1 Baines, Peter G.
1 Becker, Janet M.
1 Benney, David J.
1 Bezen, Alexandre
1 Brovchenko, Igor O.
1 Chan, Ka Hou
1 Choi, Byung Ho
1 Clift, Rebecca
1 Clutterbuck, Julie
1 Ding, Ejiang
1 Erdélyi, Róbert
1 Fitz-Gerald, Gary F.
1 Fochesato, Christophe
1 Fokas, Athanassios S.
1 Fornberg, Bengt
1 Fu, Yibin
1 Gan, Jiaye
1 Ghrist, Michelle L.
1 Gorshkov, Konstantin A.
1 Gou, S.-C.
1 He, Linyun
1 Horng, Tzyy-Leng
1 Iooss, Gérard
1 Jacobs, Patricia A.
1 Joshi, Nalini
1 Kamachi, M.
1 Kuo, Yen-Hung
1 Kuznetsov, Evgeniĭ Aleksandrovich
1 Kuznetsova, E. P.
1 Lin, Tsung-Chi
1 Liu, Tianyang
1 Lu, Zhiming
1 Maderich, Vladimir
1 Melville, W. Kendall
1 Miller, Peter D.
1 Moore, K. R.
1 Nakkeeran, K.
1 Nitsche, Martin
1 Owen, Alex
1 Pastrone, Franco
1 Poon, Chung Keung
1 Rottman, James W.
1 Ruderman, Michael S.
1 Saffman, Philip Geoffrey
...and 23 more Co-Authors
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Serials

51 Journal of Fluid Mechanics
39 Studies in Applied Mathematics
17 Physica D
13 Physics of Fluids
12 Wave Motion
9 Journal of the Australian Mathematical Society, Series B
9 Chaos
8 Physics Letters. A
6 Physics of Fluids
5 Geophysical and Astrophysical Fluid Dynamics
4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
4 SIAM Journal on Applied Mathematics
3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
3 European Journal of Mechanics. B. Fluids
2 IMA Journal of Applied Mathematics
2 Journal of Mathematical Physics
2 Fluid Dynamics Research
2 Mathematika
2 Differential Equations and Dynamical Systems
2 Proceedings of the Cambridge Philosophical Society
1 Communications on Pure and Applied Mathematics
1 Journal of Computational Physics
1 Journal of Engineering Mathematics
1 Journal of the Institute of Mathematics and its Applications
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Quarterly Journal of Mechanics and Applied Mathematics
1 Theoretical and Mathematical Physics
1 Physics of Fluids, A
1 Theoretical and Computational Fluid Dynamics
1 Mathematics and Computers in Simulation
1 Philosophical Transactions of the Royal Society of London. Ser. A
1 Journal of Physics A: Mathematical and General
1 Acta Mechanica Sinica. (English Edition)
1 The Canadian Applied Mathematics Quarterly
1 Discrete and Continuous Dynamical Systems
1 Nonlinear Dynamics
1 Physical Review Letters
1 Physica Scripta
1 The ANZIAM Journal
1 Nonlinear Analysis. Real World Applications
1 GAMM-Mitteilungen
1 CISM International Centre for Mechanical Sciences. Courses and Lectures
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences

Publications by Year

Citations contained in zbMATH

201 Publications have been cited 2,014 times in 1,284 Documents Cited by Year
Resonant flow of a stratified fluid over topography. Zbl 0614.76108
Grimshaw, R. H. J.; Smyth, N.
103
1986
Nonlinear instability at the interface between two viscous fluids. Zbl 0565.76051
Hooper, A. P.; Grimshaw, R.
78
1985
Weak and strong interactions between internal solitary waves. Zbl 0548.76020
Gear, J. A.; Grimshaw, R.
72
1984
The solitary wave in water of variable depth. II. Zbl 0222.76017
Grimshaw, R.
61
1971
The modulation of an internal gravity-wave packet, and the resonance with the mean motion. Zbl 0361.76029
Grimshaw, R. H. J.
56
1977
Slowly varying solitary waves. I: Korteweg-de Vries equation. Zbl 0414.76017
Grimshaw, R.
50
1979
Unsteady undular bores in fully nonlinear shallow-water theory. Zbl 1185.76454
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
49
2006
Weakly nonlocal solitary waves in a singularly perturbed Korteweg-de Vries equation. Zbl 0814.34043
Grimshaw, Roger; Joshi, Nalini
45
1995
Evolution equations for weakly nonlinear, long internal waves in a rotating fluid. Zbl 0572.76102
Grimshaw, R.
45
1985
Solitary internal waves with oscillatory tails. Zbl 0754.76014
Akylas, T. R.; Grimshaw, R. H. J.
37
1992
Nonlinear ordinary differential equations. Zbl 0743.34002
Grimshaw, R.
37
1990
Evolution equations for long, nonlinear internal waves in stratified shear flows. Zbl 0492.76035
Grimshaw, R.
32
1981
Approximate analytical and numerical solutions of the stationary Ostrovsky equation. Zbl 0843.76008
Gilman, O. A.; Grimshaw, R.; Stepanyants, Yu. A.
31
1995
A second-order theory for solitary waves in shallow fluids. Zbl 0508.76035
Gear, J. A.; Grimshaw, R.
27
1983
The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation. Zbl 0791.35119
Benilov, E. S.; Grimshaw, R.; Kuznetsova, E. P.
26
1993
Terminal damping of a solitary wave due to radiation in rotational systems. Zbl 1136.76334
Grimshaw, R. H. J.; He, J. -M.; Ostrovsky, L. A.
24
1998
Periodic and chaotic behaviour in a reduction of the perturbed Korteweg- de Vries equation. Zbl 0810.65078
Grimshaw, R.; Tian, X.
23
1994
Integrable shallow-water equations and undular bores. Zbl 1152.76329
El, G. A.; Grimshaw, R. H. J.; Pavlov, M. V.
22
2001
Solitary waves with damped oscillatory tails: An analysis of the fifth- order Korteweg-de Vries equation. Zbl 0824.35113
Grimshaw, R.; Malomed, B.; Benilov, E.
22
1994
Finite-amplitude solitary waves at the interface between two homogeneous fluids. Zbl 0656.76083
Pullin, D. I.; Grimshaw, R. H. J.
22
1988
The solitary wave in water of variable depth. Zbl 0193.27304
Grimshaw, R.
22
1970
Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation. Zbl 1331.35323
Mu, Gui; Qin, Zhenyun; Grimshaw, Roger
21
2015
Interactions of breathers and solitons in the extended Korteweg-de Vries equation. Zbl 1231.35196
Chow, K. W.; Grimshaw, R. H. J.; Ding, E.
21
2005
Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity. Zbl 0933.35169
Grimshaw, Roger; Polinovsky, Efim; Talipova, Tatjana
21
1999
Structural transformation of eigenvalues for a perturbed algebraic soliton potential. Zbl 1043.35522
Pelinovsky, Dmitry E.; Grimshaw, Roger H. J.
19
1997
Interfacial progressive gravity waves in a two-layer shear flow. Zbl 0569.76023
Pullin, D. I.; Grimshaw, R. H. J.
19
1983
Slowly varying solitary waves. II: Nonlinear Schrödinger equation. Zbl 0416.76014
Grimshaw, R.
19
1979
Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction. Zbl 1122.76021
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
18
2007
Generation of large-amplitude solitons in the extended Korteweg-de Vries equation. Zbl 1080.35532
Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Slunyaev, Alexey
18
2002
Slowly varying solitary wave solutions of the perturbed Korteweg-de Vries equation revisited. Zbl 0783.35062
Grimshaw, R.; Mitsudera, H.
18
1993
Resonant flow of a rotating fluid past an obstacle: The general case. Zbl 0708.76140
Grimshaw, R.
18
1990
Global existence of small-norm solutions in the reduced Ostrovsky equation. Zbl 1277.35008
Grimshaw, Roger; Pelinovsky, Dmitry
17
2014
Travelling wave solutions of the Kuramoto-Sivashinsky equation. Zbl 0692.35142
Hooper, A. P.; Grimshaw, R.
17
1988
Interaction of two lump solitons described by the Kadomtsev-Petviashvili equation. Zbl 1163.74397
Lu, Zhiming; Tian, Emily M.; Grimshaw, Roger
16
2004
Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity. Zbl 1311.35218
Grimshaw, R.; Slunyaev, A.; Pelinovsky, E.
15
2010
Long-time solutions of the Ostrovsky equation. Zbl 1194.35366
Grimshaw, Roger; Helfrich, Karl
15
2008
Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory. Zbl 1155.35424
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
15
2008
Wave group dynamics in weakly nonlinear long-wave models. Zbl 1006.76012
Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Talipova, Tatiana
15
2001
Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid. Zbl 0524.76087
Pullin, D. I.; Grimshaw, R. H. J.
15
1983
The modulation of nonlinear periodic wavetrains by dissipative terms in the Korteweg-de Vries equation. Zbl 0968.35519
Myint, S.; Grimshaw, R.
14
1995
Resonant generation of finite-amplitude waves by the flow of a uniformly stratified fluid over topography. Zbl 0850.76808
Grimshaw, Roger; Yi, Zengxin
14
1991
The reduced Ostrovsky equation: integrability and breaking. Zbl 1291.35019
Grimshaw, R. H. J.; Helfrich, Karl; Johnson, E. R.
13
2012
Solitary waves with a vortex core in a shallow layer of stratified fluid. Zbl 1185.76911
Derzho, Oleg G.; Grimshaw, Roger
13
1997
On the derivation of the modified Kadomtsev-Petviashvili equation. Zbl 0689.35082
Grimshaw, R.; Melville, W. K.
13
1989
Stability of finite-amplitude interfacial waves. I. Modulational instability for small-amplitude waves. II. Numerical results. Zbl 0614.76020
Grimshaw, R. H. J.; Pullin, D. I.
13
1985
Transcritical shallow-water flow past topography: finite-amplitude theory. Zbl 1183.76623
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
12
2009
Damping of large-amplitude solitary waves. Zbl 1163.74362
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana
12
2003
Interaction of a solitary wave with an external force. Zbl 0826.35109
Grimshaw, Roger; Pelinovsky, Efim; Tian, Xin
12
1994
Long nonlinear internal waves in channels of arbitrary cross-section. Zbl 0374.76023
Grimshaw, R. H. J.
12
1978
Analytic model for a weakly dissipative shallow-water undular bore. Zbl 1144.37342
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
11
2005
Solitary waves of a coupled Korteweg-de Vries system. Zbl 1013.35073
Grimshaw, Roger; Iooss, Gerard
11
2003
On the generation of solitons and breathers in the modified Korteweg-de Vries equation. Zbl 0970.35124
Clarke, Simon; Grimshaw, Roger; Miller, Peter; Pelinovsky, Efim; Talipova, Tatiana
11
2000
Edge waves: a long-wave theory for oceans of finite depth. Zbl 0277.76021
Grimshaw, R.
11
1974
The effect of rotation on internal solitary waves. Zbl 1250.35157
Grimshaw, Roger; Helfrich, Karl
10
2012
Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth. Zbl 1183.76228
Grimshaw, Roger; Maleewong, Montri; Asavanant, Jack
10
2009
Rossby elevation waves in the presence of a critical layer. Zbl 1386.76049
Caillol, P.; Grimshaw, R. H.
10
2008
Generation of solitary waves by transcritical flow over a step. Zbl 1141.76355
Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
10
2007
Internal solitary waves in a variable medium. Zbl 1121.76015
Grimshaw, Roger
10
2007
The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation. Zbl 0775.35008
Grimshaw, R.; Hooper, A. P.
10
1991
A coupled “AB” system: Rogue waves and modulation instabilities. Zbl 1374.35391
Wu, C. F.; Grimshaw, R. H. J.; Chow, K. W.; Chan, H. N.
9
2015
On strongly interacting internal waves in a rotating Ocean and coupled Ostrovsky equations. Zbl 1331.37127
Alias, A.; Grimshaw, R. H. J.; Khusnutdinova, K. R.
9
2013
Transcritical flow past an obstacle. Zbl 1452.76007
Grimshaw, R.
9
2010
Generation of undular bores in the shelves of slowly-varying solitary waves. Zbl 1080.76506
El, G. A.; Grimshaw, R. H. J.
9
2002
An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations. Zbl 0885.35112
Pelinovsky, Dmitry E.; Grimshaw, Roger H. J.
9
1996
Oblique interactions between internal solitary waves. Zbl 0813.76091
Grimshaw, R.; Zhu, Y.
9
1994
A note on the interaction between solitary waves in a singularly- perturbed Korteweg-de Vries equation. Zbl 0795.35103
Grimshaw, Roger; Malomed, Boris A.
9
1993
Stability of finite-amplitude interfacial waves. III. The effect of basic current shear for one-dimensional instabilities. Zbl 0642.76056
Pullin, D. I.; Grimshaw, R. H. J.
9
1986
Linearly coupled, slowly varying oscillators. Zbl 0412.34057
Grimshaw, R.; Allen, J. S.
9
1979
Nonlinear aspects of long shelf waves. Zbl 0353.76073
Grimshaw, R.
9
1977
Propagation of surface waves at high frequencies. Zbl 0157.56402
Grimshaw, R.
9
1968
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation. Zbl 1294.76079
Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.
8
2013
Wave breaking and the generation of undular bores in an integrable shallow water system. Zbl 1145.76327
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
8
2005
Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Zbl 1106.35079
Fochesato, Christophe; Dias, Frédéric; Grimshaw, Roger
8
2005
Free-surface flow under gravity and surface tension due to an applied pressure distribution. I: Bond number greater than one-third. Zbl 1112.76317
Maleewong, Montri; Asavanant, Jack; Grimshaw, Roger
8
2005
Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model. Zbl 1184.76196
Grimshaw, R. H. J.; Chan, K. H.; Chow, K. W.
8
2002
Adjustment processes and radiating solitary waves in a regularised Ostrovsky equation. Zbl 0929.76025
Grimshaw, R. H. J.
8
1999
Parametric envelope solitons in coupled Korteweg-de Vries equations. Zbl 0962.35506
Gottwald, Georg; Grimshaw, Roger; Malomed, Boris
8
1997
Numerical simulations of uniformly stratified fluid flow over topography. Zbl 0885.76084
Rottman, James W.; Broutman, Dave; Grimshaw, Roger
8
1996
Weakly nonlocal solitary waves in a singularly perturbed nonlinear Schrödinger equation. Zbl 0826.35117
Grimshaw, R.
8
1995
Resonantly generated internal waves in a contraction. Zbl 0814.76024
Clarke, S. R.; Grimshaw, R. H. J.
8
1994
A second-order theory for solitary waves in deep fluids. Zbl 0476.76029
Grimshaw, R.
8
1981
Nonlinear internal gravity waves in a rotating fluid. Zbl 0319.76021
Grimshaw, R.
8
1975
Internal gravity waves: Critical layer absorption in a rotating fluid. Zbl 0314.76021
Grimshaw, R.
8
1975
Interaction of a large amplitude interfacial solitary wave of depression with a bottom step. Zbl 1190.76083
Maderich, Vladimir; Talipova, Tatiana; Grimshaw, Roger; Terletska, Katherina; Brovchenko, Igor; Pelinovsky, Efim; Choi, Byung Ho
7
2010
Steady transcritical flow over a hole: parametric map of solutions of the forced Korteweg-de Vries equation. Zbl 1190.76034
Ee, Bernard K.; Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
7
2010
Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. Zbl 1151.76399
Akylas, T. R.; Grimshaw, R. H. J.; Clarke, S. R.; Tabaei, Ali
7
2007
Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system. Zbl 1091.35081
Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R.
7
2006
Steady multipolar planar vortices with nonlinear critical layers. Zbl 1206.86006
Caillol, P.; Grimshaw, R.
7
2004
New type of gap soliton in a coupled Korteweg-de Vries wave system. Zbl 0973.78503
Grimshaw, Roger; Malomed, Boris A.
7
1994
The rotation-modified Kadomtsev-Petviashvili equation: An analytical and numerical study. Zbl 0715.65094
Grimshaw, R.; Tang, S.
7
1990
Modulation of an internal gravity wave packet in a stratified shear flow. Zbl 0488.76028
Grimshaw, R.
7
1981
On steady recirculating flows. Zbl 0183.54505
Grimshaw, R.
7
1969
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems. Zbl 1298.37057
Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.
6
2013
Water wave packets over variable depth. Zbl 1217.35172
Grimshaw, R. H. J.; Annenkov, S. Y.
6
2011
Transcritical flow over a hole. Zbl 1177.37068
Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
6
2009
Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Zbl 1145.35446
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana; Ruderman, Michael; Erdélyi, Róbert
6
2005
On the long-term evolution of an intense localized divergent vortex on the beta-plane. Zbl 1003.76015
Reznik, G. M.; Grimshaw, R.; Benilov, E. S.
6
2000
Solitary wave transformation due to a change in polarity. Zbl 1020.35084
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatjana
6
1998
Nonlocal models for envelope waves in a stratified fluid. Zbl 0878.35091
Pelinovsky, Dmitry E.; Grimshaw, Roger H. J.
6
1996
A spectral transform for the intermediate nonlinear Schrödinger equation. Zbl 0845.35119
Pelinovsky, Dmitry E.; Grimshaw, Roger H. J.
6
1995
High-order rogue waves and their dynamics of the Fokas-Lenells equation revisited: a variable separation technique. Zbl 1430.37081
Wang, Zihao; He, Linyun; Qin, Zhenyun; Grimshaw, Roger; Mu, Gui
1
2019
Generation of mode 2 internal waves by the interaction of mode 1 waves with topography. Zbl 1430.76099
Liu, Zihua; Grimshaw, Roger; Johnson, Edward
1
2019
The evolution of second mode internal solitary waves over variable topography. Zbl 1419.76117
Yuan, C.; Grimshaw, R.; Johnson, E.
4
2018
Internal solitary wave generation by tidal flow over topography. Zbl 1419.76113
Grimshaw, R.; Helfrich, K. R.
2
2018
Decay of Kadomtsev-Petviashvili lumps in dissipative media. Zbl 1381.35010
Clarke, S.; Gorshkov, K.; Grimshaw, R.; Stepanyants, Y.
2
2018
Decay of Benjamin-Ono solitons under the influence of dissipation. Zbl 07214059
Grimshaw, Roger H.; Smyth, Noel F.; Stepanyants, Yury A.
1
2018
Topographic effect on oblique internal wave-wave interactions. Zbl 1415.76114
Yuan, C.; Grimshaw, R.; Johnson, E.; Wang, Zhan
1
2018
Radiating solitary waves in coupled Boussinesq equations. Zbl 1404.35089
Grimshaw, R. H. J.; Khusnutdinova, K. R.; Moore, K. R.
3
2017
Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion. Zbl 1371.35250
Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani
5
2016
Transcritical flow over two obstacles: forced Korteweg-de Vries framework. Undular bore. Zbl 1383.76065
Grimshaw, Roger H. J.; Maleewong, Montri
4
2016
The propagation of internal undular bores over variable topography. Zbl 1415.35240
Grimshaw, R.; Yuan, C.
2
2016
Nonlinear wave equations for oceanic internal solitary waves. Zbl 1332.35287
Grimshaw, Roger
1
2016
Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation. Zbl 1331.35323
Mu, Gui; Qin, Zhenyun; Grimshaw, Roger
21
2015
A coupled “AB” system: Rogue waves and modulation instabilities. Zbl 1374.35391
Wu, C. F.; Grimshaw, R. H. J.; Chow, K. W.; Chan, H. N.
9
2015
Critical control in transcritical shallow-water flow over two obstacles. Zbl 1382.76031
Grimshaw, Roger H. J.; Maleewong, Montri
2
2015
Change of polarity for periodic waves in the variable-coefficient Korteweg-de Vries equation. Zbl 1314.35140
Grimshaw, Roger
1
2015
Global existence of small-norm solutions in the reduced Ostrovsky equation. Zbl 1277.35008
Grimshaw, Roger; Pelinovsky, Dmitry
17
2014
On strongly interacting internal waves in a rotating Ocean and coupled Ostrovsky equations. Zbl 1331.37127
Alias, A.; Grimshaw, R. H. J.; Khusnutdinova, K. R.
9
2013
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation. Zbl 1294.76079
Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.
8
2013
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems. Zbl 1298.37057
Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.
6
2013
Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth. Zbl 1320.76049
Grimshaw, Roger; Maleewong, Montri
2
2013
The reduced Ostrovsky equation: integrability and breaking. Zbl 1291.35019
Grimshaw, R. H. J.; Helfrich, Karl; Johnson, E. R.
13
2012
The effect of rotation on internal solitary waves. Zbl 1250.35157
Grimshaw, Roger; Helfrich, Karl
10
2012
Transformation of a shoaling undular bore. Zbl 1275.76054
El, G. A.; Grimshaw, R. H. J.; Tiong, W. K.
4
2012
Water wave packets over variable depth. Zbl 1217.35172
Grimshaw, R. H. J.; Annenkov, S. Y.
6
2011
Steady transcritical flow over an obstacle: parametric map of solutions of the forced extended Korteweg-de Vries equation. Zbl 1308.76033
Ee, Bernard K.; Grimshaw, R. H. J.; Chow, K. W.; Zhang, D-H.
2
2011
Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity. Zbl 1311.35218
Grimshaw, R.; Slunyaev, A.; Pelinovsky, E.
15
2010
Transcritical flow past an obstacle. Zbl 1452.76007
Grimshaw, R.
9
2010
Interaction of a large amplitude interfacial solitary wave of depression with a bottom step. Zbl 1190.76083
Maderich, Vladimir; Talipova, Tatiana; Grimshaw, Roger; Terletska, Katherina; Brovchenko, Igor; Pelinovsky, Efim; Choi, Byung Ho
7
2010
Steady transcritical flow over a hole: parametric map of solutions of the forced Korteweg-de Vries equation. Zbl 1190.76034
Ee, Bernard K.; Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
7
2010
Evolution of solitary waves in a two-pycnocline system. Zbl 1183.76650
Nitsche, M.; Weidman, P. D.; Grimshaw, R.; Ghrist, M.; Fornberg, B.
5
2010
Homogenization of the variable-speed wave equation. Zbl 1231.76242
Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim
3
2010
Exponential asymptotics and generalized solitary waves. Zbl 1321.76014
Grimshaw, Roger
3
2010
Steady gap solitons in a coupled Korteweg-de Vries system: A dynamical systems approach. Zbl 1186.37077
Grimshaw, Roger; Christodoulides, Paul
2
2010
Structure formation in the oceanic subsurface bubble layer by an internal wave field. Zbl 1308.86004
Grimshaw, R. H. J.; Khusnutdinova, K. R.; Ostrovsky, L. A.; Topolnikov, A. S.
1
2010
Transcritical shallow-water flow past topography: finite-amplitude theory. Zbl 1183.76623
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
12
2009
Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth. Zbl 1183.76228
Grimshaw, Roger; Maleewong, Montri; Asavanant, Jack
10
2009
Transcritical flow over a hole. Zbl 1177.37068
Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
6
2009
Long-time solutions of the Ostrovsky equation. Zbl 1194.35366
Grimshaw, Roger; Helfrich, Karl
15
2008
Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory. Zbl 1155.35424
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
15
2008
Rossby elevation waves in the presence of a critical layer. Zbl 1386.76049
Caillol, P.; Grimshaw, R. H.
10
2008
Nonlinear free surface flows past a semi-infinite flat plate in water of finite depth. Zbl 1182.76484
Maleewong, M.; Grimshaw, R. H. J.
4
2008
Rossby solitary waves in the presence of a critical layer. Zbl 1207.76044
Caillol, Philippe; Grimshaw, Roger H.
3
2008
Gap-solitons in a three-layered stratified flow. Zbl 1231.76062
Grimshaw, Roger; Christodoulides, Paul
2
2008
The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation. Zbl 1181.76040
Grimshaw, R. H. J.; Khusnutdinova, K. R.; Ostrovsky, L. A.
1
2008
Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction. Zbl 1122.76021
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
18
2007
Generation of solitary waves by transcritical flow over a step. Zbl 1141.76355
Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W.
10
2007
Internal solitary waves in a variable medium. Zbl 1121.76015
Grimshaw, Roger
10
2007
Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. Zbl 1151.76399
Akylas, T. R.; Grimshaw, R. H. J.; Clarke, S. R.; Tabaei, Ali
7
2007
Solitary waves in fluids. Zbl 1106.76007
Grimshaw, R. H. J. (ed.)
5
2007
Solitary waves propagating over variable topography. Zbl 1310.76043
Grimshaw, Roger
4
2007
Asymmetric internal solitary waves with a trapped core in deep fluids. Zbl 1182.76201
Derzho, Oleg G.; Grimshaw, Roger
2
2007
Solitary wave solution for a non-integrable, variable coefficient nonlinear Schrödinger equation. Zbl 1118.35355
Grimshaw, R.; Nakkeeran, K.; Poon, C. K.; Chow, K. W.
2
2007
Envelope solitary waves. Zbl 1316.76026
Grimshaw, R. H. J.
1
2007
Unsteady undular bores in fully nonlinear shallow-water theory. Zbl 1185.76454
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F.
49
2006
Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system. Zbl 1091.35081
Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R.
7
2006
Interactions of breathers and solitons in the extended Korteweg-de Vries equation. Zbl 1231.35196
Chow, K. W.; Grimshaw, R. H. J.; Ding, E.
21
2005
Analytic model for a weakly dissipative shallow-water undular bore. Zbl 1144.37342
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
11
2005
Wave breaking and the generation of undular bores in an integrable shallow water system. Zbl 1145.76327
El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M.
8
2005
Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Zbl 1106.35079
Fochesato, Christophe; Dias, Frédéric; Grimshaw, Roger
8
2005
Free-surface flow under gravity and surface tension due to an applied pressure distribution. I: Bond number greater than one-third. Zbl 1112.76317
Maleewong, Montri; Asavanant, Jack; Grimshaw, Roger
8
2005
Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Zbl 1145.35446
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana; Ruderman, Michael; Erdélyi, Róbert
6
2005
Rossby waves on a shear flow with recirculation cores. Zbl 1145.76339
Derzho, Oleg G.; Grimshaw, Roger
5
2005
Free surface flow under gravity and surface tension due to an applied pressure distribution. II: Bond number less than one-third. Zbl 1065.76021
Maleewong, Montri; Grimshaw, Roger; Asavanant, Jack
5
2005
Nonlinear waves in fluids: Recent advances and modern applications. CISM summer school, Udine, Italy, September 20–24, 2004. Zbl 1084.76004
Grimshaw, Roger (ed.)
2
2005
Solitons in nonintegrable systems. Zbl 1144.37350
Grimshaw, Roger H. J.; Ostrovsky, Lev A.; Pelinovsky, Dmitry E.
1
2005
Soliton dynamics in a strong periodic field: the Korteweg-de Vries framework. Zbl 1194.35367
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana
1
2005
Korteweg-de Vries equation. Zbl 1095.76013
Grimshaw, Roger
1
2005
Interaction of two lump solitons described by the Kadomtsev-Petviashvili equation. Zbl 1163.74397
Lu, Zhiming; Tian, Emily M.; Grimshaw, Roger
16
2004
Steady multipolar planar vortices with nonlinear critical layers. Zbl 1206.86006
Caillol, P.; Grimshaw, R.
7
2004
Generation of secondary solitary waves in the variable-coefficient Korteweg-de Vries equation. Zbl 1141.35447
Grimshaw, R. H. J.; Pudjaprasetya, S. R.
4
2004
Damping of large-amplitude solitary waves. Zbl 1163.74362
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana
12
2003
Solitary waves of a coupled Korteweg-de Vries system. Zbl 1013.35073
Grimshaw, Roger; Iooss, Gerard
11
2003
The influence of modulational instability on energy exchange in coupled sine-Gordon equations. Zbl 1178.35330
Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R.
3
2003
Generation of large-amplitude solitons in the extended Korteweg-de Vries equation. Zbl 1080.35532
Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Slunyaev, Alexey
18
2002
Generation of undular bores in the shelves of slowly-varying solitary waves. Zbl 1080.76506
El, G. A.; Grimshaw, R. H. J.
9
2002
Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model. Zbl 1184.76196
Grimshaw, R. H. J.; Chan, K. H.; Chow, K. W.
8
2002
Interaction of a solitary wave with an external force in the extended Korteweg-de Vries equation. Zbl 1042.35066
Grimshaw, Roger; Pelinovsky, Efim
5
2002
Nonlinear geostrophic adjustment in the presence of a boundary. Zbl 1063.76104
Reznik, G. M.; Grimshaw, R.
4
2002
Dispersion management for solitons in a Korteweg-de Vries system. Zbl 1080.35522
Clarke, Simon; Malomed, Boris A.; Grimshaw, Roger
3
2002
Solitary waves with recirculation zones in axisymmetric rotating flows. Zbl 1029.76008
Derzho, Oleg; Grimshaw, Roger
2
2002
Nonlinear effects in wave scattering and generation. Flow interation with topography. Zbl 1187.76635
Grimshaw, R. H. J.
1
2002
Long-wave instability in a three-layer stratified shear flow. Zbl 1152.76379
Grimshaw, Roger; Skrynnikov, Yuri
1
2002
Integrable shallow-water equations and undular bores. Zbl 1152.76329
El, G. A.; Grimshaw, R. H. J.; Pavlov, M. V.
22
2001
Wave group dynamics in weakly nonlinear long-wave models. Zbl 1006.76012
Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Talipova, Tatiana
15
2001
Short-wave instability in a three-layer stratified shear flow. Zbl 0987.76029
Grimshaw, Roger; Christodoulides, Paul
3
2001
Ageostrophic dynamics of an intense localized vortex on a \(\beta\)-plane. Zbl 1046.76007
Reznik, G. M.; Grimshaw, R.
2
2001
On the generation of solitons and breathers in the modified Korteweg-de Vries equation. Zbl 0970.35124
Clarke, Simon; Grimshaw, Roger; Miller, Peter; Pelinovsky, Efim; Talipova, Tatiana
11
2000
On the long-term evolution of an intense localized divergent vortex on the beta-plane. Zbl 1003.76015
Reznik, G. M.; Grimshaw, R.; Benilov, E. S.
6
2000
Weakly nonlinear internal wave fronts trapped in contractions. Zbl 0956.76015
Clarke, S. R.; Grimshaw, R. H. J.
5
2000
Models for long-wave instability due to a resonance between two waves. Zbl 0974.76030
Grimshaw, R.
4
2000
Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity. Zbl 0933.35169
Grimshaw, Roger; Polinovsky, Efim; Talipova, Tatjana
21
1999
Adjustment processes and radiating solitary waves in a regularised Ostrovsky equation. Zbl 0929.76025
Grimshaw, R. H. J.
8
1999
Numerical simulations of internal solitary waves with vortex cores. Zbl 1051.76530
Aigner, A.; Broutman, D.; Grimshaw, R.
3
1999
The effect of weak shear on finite-amplitude internal solitary waves. Zbl 0978.76015
Clarke, S. R.; Grimshaw, R. H. J.
2
1999
Exact periodic steady solutions for nonlinear wave equations: a new approach. Zbl 0938.35129
Grimshaw, Roger; Pavlov, Maxim
2
1999
Hamiltonian formulation for solitary waves propagating on a variable background. Zbl 0934.76011
Grimshaw, R.; Pudjaprasetya, S. R.
2
1999
Passage of a wave pulse through a zero-dispersion point in the nonlinear Schrödinger equation. Zbl 1044.78508
Clarke, S. R.; Clutterbuck, Julie; Grimshaw, R. H. J.; Malomed, Boris A.
1
1999
Terminal damping of a solitary wave due to radiation in rotational systems. Zbl 1136.76334
Grimshaw, R. H. J.; He, J. -M.; Ostrovsky, L. A.
24
1998
Solitary wave transformation due to a change in polarity. Zbl 1020.35084
Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatjana
6
1998
...and 101 more Documents
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Cited by 1,692 Authors

110 Grimshaw, Roger Hamilton James
22 Pelinovsky, Dmitry Efimovich
19 El, Gennady A.
19 Pelinovsky, Efim
17 Gao, Yitian
15 Akylas, T. R.
14 Khusnutdinova, Karima Robertovna
14 Stepanyants, Yury A.
13 Pazoto, Ademir Fernando
13 Smyth, Noel F.
13 Vanden-Broeck, Jean-Marc
12 Boyd, John Philip
12 Dias, Frédéric
12 Hoefer, Mark A.
12 Stastna, Marek
11 Chow, Kwok Wing
11 Dutykh, Denys
11 Johnson, Edward Robert
11 Tian, Bo
10 Liu, Yue
10 Milewski, Paul A.
10 Talipova, Tatiana
9 Coclite, Giuseppe Maria
9 Gavrilyuk, Sergey L.
9 Malomed, Boris A.
8 Champneys, Alan R.
8 Forbes, Lawrence K.
8 Hanazaki, Hideshi
8 He, Jingsong
8 Kalisch, Henrik
8 Liu, Philip L.-F.
8 Maleewong, Montri
8 Marchant, Tim R.
8 Mitsotakis, Dimitrios E.
8 Xin, Jie
7 Binder, Benjamin James
7 Clarke, Simon R.
7 Derzho, Oleg G.
7 Di Ruvo, Lorenzo
7 Helfrich, Karl R.
7 Il’ichev, Andreĭ Teĭmurazovich
7 Kamchatnov, Anatoly M.
7 Lü, Xing
7 Lustri, Christopher J.
7 Muñoz, Claudio
7 Yang, Jianke
7 Yu, Xin
7 Zhang, Ruigang
7 Zhu, Yong
6 Alejo, Miguel A.
6 Bakholdin, Igor B.
6 Bona, Jerry Lloyd
6 Cui, Shangbin
6 Lamb, Kevin G.
6 Papageorgiou, Demetrios T.
6 Pedersen, Geir Kleivstul
6 Shen, Samuel Shan-Pu
6 Yang, Liangui
6 Yeh, Harry H.
5 Blyth, Mark G.
5 Choi, Wooyoung
5 Feng, Baofeng
5 Gao, Peng
5 Geng, Xianguo
5 Kurkin, Andrey
5 Liu, Ying
5 Ma, Wen-Xiu
5 Ratliff, Daniel J.
5 Reznik, Gregory M.
5 Saut, Jean-Claude
5 Soontiens, Nancy
5 Sun, Zhiyuan
5 Wilson, Dan D.
5 Xu, Tao
5 Yan, Wei
4 Ablowitz, Mark Jay
4 Belward, Shaun R.
4 Biondini, Gino
4 Bridges, Thomas J.
4 Capistrano-Filho, Roberto A.
4 Chapman, Stephen Jonathan
4 Chen, Mo
4 Christodoulides, Paul
4 Clamond, Didier
4 Curtis, Christopher W.
4 Daripa, Prabir K.
4 Dong, Huanhe
4 Duran, Angel
4 Eames, Ian
4 Ee, Bernard K.
4 Esler, J. G.
4 Guo, Boling
4 Hattam, L. L.
4 Hooper, Alison P.
4 Kalogirou, Anna
4 Kataoka, Takeshi
4 Khalique, Chaudry Masood
4 Klettner, Christian A.
4 Liu, Quansheng
4 Meng, Xianghua
...and 1,592 more Authors
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Cited in 192 Serials

182 Journal of Fluid Mechanics
78 Wave Motion
73 Physica D
73 Physics of Fluids
69 Studies in Applied Mathematics
37 Chaos
37 European Journal of Mechanics. B. Fluids
34 Applied Mathematics and Computation
25 Journal of Mathematical Physics
25 Nonlinear Dynamics
23 Physics of Fluids, A
22 Fluid Dynamics
20 Chaos, Solitons and Fractals
20 Communications in Nonlinear Science and Numerical Simulation
17 Applied Mathematics Letters
16 Journal of Differential Equations
15 Computers & Mathematics with Applications
15 Journal of Mathematical Analysis and Applications
15 Physics Letters. A
13 Journal of Computational Physics
13 Mathematics and Computers in Simulation
12 Computers and Fluids
12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
10 Acta Mechanica
10 Theoretical and Mathematical Physics
10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 Nonlinearity
8 Applied Mathematical Modelling
7 Communications in Mathematical Physics
7 Geophysical and Astrophysical Fluid Dynamics
7 Journal of Engineering Mathematics
7 Theoretical and Computational Fluid Dynamics
7 Journal of Computational and Applied Mathematics
7 Applied Mathematics and Mechanics. (English Edition)
7 Journal of Scientific Computing
7 Nonlinear Analysis. Real World Applications
6 Quarterly of Applied Mathematics
6 European Journal of Applied Mathematics
6 SIAM Journal on Mathematical Analysis
6 Journal of Nonlinear Science
6 Advances in Difference Equations
6 Izvestiya. Atmospheric and Oceanic Physics
5 International Journal of Theoretical Physics
5 Mathematical Methods in the Applied Sciences
5 Physics of Fluids
5 Acta Applicandae Mathematicae
5 Mathematical Problems in Engineering
5 Abstract and Applied Analysis
5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
5 Acta Mathematica Sinica. English Series
5 Communications in Contemporary Mathematics
5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
4 International Journal of Engineering Science
4 International Journal for Numerical Methods in Fluids
4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
4 Discrete and Continuous Dynamical Systems
4 The ANZIAM Journal
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4 Evolution Equations and Control Theory
3 International Journal of Modern Physics B
3 Applicable Analysis
3 Archive for Rational Mechanics and Analysis
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3 NoDEA. Nonlinear Differential Equations and Applications
3 Journal of Shanghai University
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3 Discrete and Continuous Dynamical Systems. Series B
3 Mediterranean Journal of Mathematics
3 Discrete and Continuous Dynamical Systems. Series S
3 Communications in Theoretical Physics
3 Journal of Theoretical Biology
3 Water Waves
2 Computer Physics Communications
2 Communications on Pure and Applied Mathematics
2 Journal of Statistical Physics
2 Mathematical Notes
2 Reports on Mathematical Physics
2 Applied Mathematics and Optimization
2 BIT
2 Journal of Functional Analysis
2 Meccanica
2 SIAM Journal on Control and Optimization
2 Systems & Control Letters
2 Chinese Annals of Mathematics. Series B
2 Applied Mathematics. Series B (English Edition)
2 Computational and Applied Mathematics
2 Journal of Inverse and Ill-Posed Problems
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Cited in 43 Fields

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718 Partial differential equations (35-XX)
210 Dynamical systems and ergodic theory (37-XX)
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7 Global analysis, analysis on manifolds (58-XX)
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