Edit Profile Grimshaw, Roger Hamilton James Compute Distance To: Compute Author ID: grimshaw.roger-h-j 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, Tzy-Chy 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 all top 5 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 all top 5 Fields 176 Fluid mechanics (76-XX) 125 Partial differential equations (35-XX) 37 Geophysics (86-XX) 31 Dynamical systems and ergodic theory (37-XX) 12 Ordinary differential equations (34-XX) 8 Numerical analysis (65-XX) 6 Optics, electromagnetic theory (78-XX) 5 Mechanics of particles and systems (70-XX) 3 Mechanics of deformable solids (74-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Biology and other natural sciences (92-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 201 Publications have been cited 2,013 times in 1,283 Documents Cited by ▼ Year ▼ Resonant flow of a stratified fluid over topography. Zbl 0614.76108Grimshaw, R. H. J.; Smyth, N. 103 1986 Nonlinear instability at the interface between two viscous fluids. Zbl 0565.76051Hooper, A. P.; Grimshaw, R. 78 1985 Weak and strong interactions between internal solitary waves. Zbl 0548.76020Gear, J. A.; Grimshaw, R. 72 1984 The solitary wave in water of variable depth. II. Zbl 0222.76017Grimshaw, R. 61 1971 The modulation of an internal gravity-wave packet, and the resonance with the mean motion. Zbl 0361.76029Grimshaw, R. H. J. 55 1977 Slowly varying solitary waves. I: Korteweg-de Vries equation. Zbl 0414.76017Grimshaw, R. 50 1979 Unsteady undular bores in fully nonlinear shallow-water theory. Zbl 1185.76454El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. 49 2006 Weakly nonlocal solitary waves in a singularly perturbed Korteweg-de Vries equation. Zbl 0814.34043Grimshaw, Roger; Joshi, Nalini 45 1995 Evolution equations for weakly nonlinear, long internal waves in a rotating fluid. Zbl 0572.76102Grimshaw, R. 45 1985 Solitary internal waves with oscillatory tails. Zbl 0754.76014Akylas, T. R.; Grimshaw, R. H. J. 37 1992 Nonlinear ordinary differential equations. Zbl 0743.34002Grimshaw, R. 37 1990 Evolution equations for long, nonlinear internal waves in stratified shear flows. Zbl 0492.76035Grimshaw, R. 32 1981 Approximate analytical and numerical solutions of the stationary Ostrovsky equation. Zbl 0843.76008Gilman, O. A.; Grimshaw, R.; Stepanyants, Yu. A. 31 1995 A second-order theory for solitary waves in shallow fluids. Zbl 0508.76035Gear, J. A.; Grimshaw, R. 27 1983 The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation. Zbl 0791.35119Benilov, E. S.; Grimshaw, R.; Kuznetsova, E. P. 26 1993 Terminal damping of a solitary wave due to radiation in rotational systems. Zbl 1136.76334Grimshaw, 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 0810.65078Grimshaw, R.; Tian, X. 23 1994 Integrable shallow-water equations and undular bores. Zbl 1152.76329El, 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 0824.35113Grimshaw, R.; Malomed, B.; Benilov, E. 22 1994 Finite-amplitude solitary waves at the interface between two homogeneous fluids. Zbl 0656.76083Pullin, D. I.; Grimshaw, R. H. J. 22 1988 The solitary wave in water of variable depth. Zbl 0193.27304Grimshaw, R. 22 1970 Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation. Zbl 1331.35323Mu, Gui; Qin, Zhenyun; Grimshaw, Roger 21 2015 Interactions of breathers and solitons in the extended Korteweg-de Vries equation. Zbl 1231.35196Chow, 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 0933.35169Grimshaw, Roger; Polinovsky, Efim; Talipova, Tatjana 21 1999 Structural transformation of eigenvalues for a perturbed algebraic soliton potential. Zbl 1043.35522Pelinovsky, Dmitry E.; Grimshaw, Roger H. J. 19 1997 Interfacial progressive gravity waves in a two-layer shear flow. Zbl 0569.76023Pullin, D. I.; Grimshaw, R. H. J. 19 1983 Slowly varying solitary waves. II: Nonlinear Schrödinger equation. Zbl 0416.76014Grimshaw, R. 19 1979 Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction. Zbl 1122.76021El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M. 18 2007 Generation of large-amplitude solitons in the extended Korteweg-de Vries equation. Zbl 1080.35532Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Slunyaev, Alexey 18 2002 Slowly varying solitary wave solutions of the perturbed Korteweg-de Vries equation revisited. Zbl 0783.35062Grimshaw, R.; Mitsudera, H. 18 1993 Resonant flow of a rotating fluid past an obstacle: The general case. Zbl 0708.76140Grimshaw, R. 18 1990 Global existence of small-norm solutions in the reduced Ostrovsky equation. Zbl 1277.35008Grimshaw, Roger; Pelinovsky, Dmitry 17 2014 Travelling wave solutions of the Kuramoto-Sivashinsky equation. Zbl 0692.35142Hooper, A. P.; Grimshaw, R. 17 1988 Interaction of two lump solitons described by the Kadomtsev-Petviashvili equation. Zbl 1163.74397Lu, 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 1311.35218Grimshaw, R.; Slunyaev, A.; Pelinovsky, E. 15 2010 Long-time solutions of the Ostrovsky equation. Zbl 1194.35366Grimshaw, Roger; Helfrich, Karl 15 2008 Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory. Zbl 1155.35424El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. 15 2008 Wave group dynamics in weakly nonlinear long-wave models. Zbl 1006.76012Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Talipova, Tatiana 15 2001 Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid. Zbl 0524.76087Pullin, D. I.; Grimshaw, R. H. J. 15 1983 The modulation of nonlinear periodic wavetrains by dissipative terms in the Korteweg-de Vries equation. Zbl 0968.35519Myint, S.; Grimshaw, R. 14 1995 Resonant generation of finite-amplitude waves by the flow of a uniformly stratified fluid over topography. Zbl 0850.76808Grimshaw, Roger; Yi, Zengxin 14 1991 The reduced Ostrovsky equation: integrability and breaking. Zbl 1291.35019Grimshaw, R. H. J.; Helfrich, Karl; Johnson, E. R. 13 2012 Solitary waves with a vortex core in a shallow layer of stratified fluid. Zbl 1185.76911Derzho, Oleg G.; Grimshaw, Roger 13 1997 On the derivation of the modified Kadomtsev-Petviashvili equation. Zbl 0689.35082Grimshaw, R.; Melville, W. K. 13 1989 Stability of finite-amplitude interfacial waves. I. Modulational instability for small-amplitude waves. II. Numerical results. Zbl 0614.76020Grimshaw, R. H. J.; Pullin, D. I. 13 1985 Transcritical shallow-water flow past topography: finite-amplitude theory. Zbl 1183.76623El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. 12 2009 Damping of large-amplitude solitary waves. Zbl 1163.74362Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana 12 2003 Interaction of a solitary wave with an external force. Zbl 0826.35109Grimshaw, Roger; Pelinovsky, Efim; Tian, Xin 12 1994 Long nonlinear internal waves in channels of arbitrary cross-section. Zbl 0374.76023Grimshaw, R. H. J. 12 1978 Analytic model for a weakly dissipative shallow-water undular bore. Zbl 1144.37342El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M. 11 2005 Solitary waves of a coupled Korteweg-de Vries system. Zbl 1013.35073Grimshaw, Roger; Iooss, Gerard 11 2003 On the generation of solitons and breathers in the modified Korteweg-de Vries equation. Zbl 0970.35124Clarke, Simon; Grimshaw, Roger; Miller, Peter; Pelinovsky, Efim; Talipova, Tatiana 11 2000 Edge waves: a long-wave theory for oceans of finite depth. Zbl 0277.76021Grimshaw, R. 11 1974 The effect of rotation on internal solitary waves. Zbl 1250.35157Grimshaw, Roger; Helfrich, Karl 10 2012 Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth. Zbl 1183.76228Grimshaw, Roger; Maleewong, Montri; Asavanant, Jack 10 2009 Rossby elevation waves in the presence of a critical layer. Zbl 1386.76049Caillol, P.; Grimshaw, R. H. 10 2008 Generation of solitary waves by transcritical flow over a step. Zbl 1141.76355Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W. 10 2007 Internal solitary waves in a variable medium. Zbl 1121.76015Grimshaw, Roger 10 2007 The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation. Zbl 0775.35008Grimshaw, R.; Hooper, A. P. 10 1991 A coupled “AB” system: Rogue waves and modulation instabilities. Zbl 1374.35391Wu, 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 1331.37127Alias, A.; Grimshaw, R. H. J.; Khusnutdinova, K. R. 9 2013 Transcritical flow past an obstacle. Zbl 1452.76007Grimshaw, R. 9 2010 Generation of undular bores in the shelves of slowly-varying solitary waves. Zbl 1080.76506El, 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 0885.35112Pelinovsky, Dmitry E.; Grimshaw, Roger H. J. 9 1996 Oblique interactions between internal solitary waves. Zbl 0813.76091Grimshaw, R.; Zhu, Y. 9 1994 A note on the interaction between solitary waves in a singularly- perturbed Korteweg-de Vries equation. Zbl 0795.35103Grimshaw, Roger; Malomed, Boris A. 9 1993 Stability of finite-amplitude interfacial waves. III. The effect of basic current shear for one-dimensional instabilities. Zbl 0642.76056Pullin, D. I.; Grimshaw, R. H. J. 9 1986 Linearly coupled, slowly varying oscillators. Zbl 0412.34057Grimshaw, R.; Allen, J. S. 9 1979 Nonlinear aspects of long shelf waves. Zbl 0353.76073Grimshaw, R. 9 1977 Propagation of surface waves at high frequencies. Zbl 0157.56402Grimshaw, R. 9 1968 Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation. Zbl 1294.76079Kamchatnov, 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 1145.76327El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M. 8 2005 Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Zbl 1106.35079Fochesato, 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 1112.76317Maleewong, Montri; Asavanant, Jack; Grimshaw, Roger 8 2005 Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model. Zbl 1184.76196Grimshaw, R. H. J.; Chan, K. H.; Chow, K. W. 8 2002 Adjustment processes and radiating solitary waves in a regularised Ostrovsky equation. Zbl 0929.76025Grimshaw, R. H. J. 8 1999 Parametric envelope solitons in coupled Korteweg-de Vries equations. Zbl 0962.35506Gottwald, Georg; Grimshaw, Roger; Malomed, Boris 8 1997 Numerical simulations of uniformly stratified fluid flow over topography. Zbl 0885.76084Rottman, James W.; Broutman, Dave; Grimshaw, Roger 8 1996 Weakly nonlocal solitary waves in a singularly perturbed nonlinear Schrödinger equation. Zbl 0826.35117Grimshaw, R. 8 1995 Resonantly generated internal waves in a contraction. Zbl 0814.76024Clarke, S. R.; Grimshaw, R. H. J. 8 1994 A second-order theory for solitary waves in deep fluids. Zbl 0476.76029Grimshaw, R. 8 1981 Nonlinear internal gravity waves in a rotating fluid. Zbl 0319.76021Grimshaw, R. 8 1975 Internal gravity waves: Critical layer absorption in a rotating fluid. Zbl 0314.76021Grimshaw, R. 8 1975 Interaction of a large amplitude interfacial solitary wave of depression with a bottom step. Zbl 1190.76083Maderich, 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 1190.76034Ee, 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 1151.76399Akylas, 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 1091.35081Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R. 7 2006 Steady multipolar planar vortices with nonlinear critical layers. Zbl 1206.86006Caillol, P.; Grimshaw, R. 7 2004 New type of gap soliton in a coupled Korteweg-de Vries wave system. Zbl 0973.78503Grimshaw, Roger; Malomed, Boris A. 7 1994 The rotation-modified Kadomtsev-Petviashvili equation: An analytical and numerical study. Zbl 0715.65094Grimshaw, R.; Tang, S. 7 1990 Modulation of an internal gravity wave packet in a stratified shear flow. Zbl 0488.76028Grimshaw, R. 7 1981 On steady recirculating flows. Zbl 0183.54505Grimshaw, R. 7 1969 Two-soliton interaction as an elementary act of soliton turbulence in integrable systems. Zbl 1298.37057Pelinovsky, 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 1217.35172Grimshaw, R. H. J.; Annenkov, S. Y. 6 2011 Transcritical flow over a hole. Zbl 1177.37068Grimshaw, 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 1145.35446Grimshaw, 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 1003.76015Reznik, G. M.; Grimshaw, R.; Benilov, E. S. 6 2000 Solitary wave transformation due to a change in polarity. Zbl 1020.35084Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatjana 6 1998 Nonlocal models for envelope waves in a stratified fluid. Zbl 0878.35091Pelinovsky, Dmitry E.; Grimshaw, Roger H. J. 6 1996 A spectral transform for the intermediate nonlinear Schrödinger equation. Zbl 0845.35119Pelinovsky, 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 1430.37081Wang, 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 1430.76099Liu, Zihua; Grimshaw, Roger; Johnson, Edward 1 2019 The evolution of second mode internal solitary waves over variable topography. Zbl 1419.76117Yuan, C.; Grimshaw, R.; Johnson, E. 4 2018 Internal solitary wave generation by tidal flow over topography. Zbl 1419.76113Grimshaw, R.; Helfrich, K. R. 2 2018 Decay of Kadomtsev-Petviashvili lumps in dissipative media. Zbl 1381.35010Clarke, S.; Gorshkov, K.; Grimshaw, R.; Stepanyants, Y. 2 2018 Decay of Benjamin-Ono solitons under the influence of dissipation. Zbl 07214059Grimshaw, Roger H.; Smyth, Noel F.; Stepanyants, Yury A. 1 2018 Topographic effect on oblique internal wave-wave interactions. Zbl 1415.76114Yuan, C.; Grimshaw, R.; Johnson, E.; Wang, Zhan 1 2018 Radiating solitary waves in coupled Boussinesq equations. Zbl 1404.35089Grimshaw, 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 1371.35250Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani 5 2016 Transcritical flow over two obstacles: forced Korteweg-de Vries framework. Undular bore. Zbl 1383.76065Grimshaw, Roger H. J.; Maleewong, Montri 4 2016 The propagation of internal undular bores over variable topography. Zbl 1415.35240Grimshaw, R.; Yuan, C. 2 2016 Nonlinear wave equations for oceanic internal solitary waves. Zbl 1332.35287Grimshaw, Roger 1 2016 Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation. Zbl 1331.35323Mu, Gui; Qin, Zhenyun; Grimshaw, Roger 21 2015 A coupled “AB” system: Rogue waves and modulation instabilities. Zbl 1374.35391Wu, 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 1382.76031Grimshaw, Roger H. J.; Maleewong, Montri 2 2015 Change of polarity for periodic waves in the variable-coefficient Korteweg-de Vries equation. Zbl 1314.35140Grimshaw, Roger 1 2015 Global existence of small-norm solutions in the reduced Ostrovsky equation. Zbl 1277.35008Grimshaw, Roger; Pelinovsky, Dmitry 17 2014 On strongly interacting internal waves in a rotating Ocean and coupled Ostrovsky equations. Zbl 1331.37127Alias, 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 1294.76079Kamchatnov, 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 1298.37057Pelinovsky, 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 1320.76049Grimshaw, Roger; Maleewong, Montri 2 2013 The reduced Ostrovsky equation: integrability and breaking. Zbl 1291.35019Grimshaw, R. H. J.; Helfrich, Karl; Johnson, E. R. 13 2012 The effect of rotation on internal solitary waves. Zbl 1250.35157Grimshaw, Roger; Helfrich, Karl 10 2012 Transformation of a shoaling undular bore. Zbl 1275.76054El, G. A.; Grimshaw, R. H. J.; Tiong, W. K. 4 2012 Water wave packets over variable depth. Zbl 1217.35172Grimshaw, 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 1308.76033Ee, 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 1311.35218Grimshaw, R.; Slunyaev, A.; Pelinovsky, E. 15 2010 Transcritical flow past an obstacle. Zbl 1452.76007Grimshaw, R. 9 2010 Interaction of a large amplitude interfacial solitary wave of depression with a bottom step. Zbl 1190.76083Maderich, 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 1190.76034Ee, Bernard K.; Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W. 7 2010 Evolution of solitary waves in a two-pycnocline system. Zbl 1183.76650Nitsche, M.; Weidman, P. D.; Grimshaw, R.; Ghrist, M.; Fornberg, B. 5 2010 Homogenization of the variable-speed wave equation. Zbl 1231.76242Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim 3 2010 Exponential asymptotics and generalized solitary waves. Zbl 1321.76014Grimshaw, Roger 3 2010 Steady gap solitons in a coupled Korteweg-de Vries system: A dynamical systems approach. Zbl 1186.37077Grimshaw, Roger; Christodoulides, Paul 2 2010 Structure formation in the oceanic subsurface bubble layer by an internal wave field. Zbl 1308.86004Grimshaw, R. H. J.; Khusnutdinova, K. R.; Ostrovsky, L. A.; Topolnikov, A. S. 1 2010 Transcritical shallow-water flow past topography: finite-amplitude theory. Zbl 1183.76623El, 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 1183.76228Grimshaw, Roger; Maleewong, Montri; Asavanant, Jack 10 2009 Transcritical flow over a hole. Zbl 1177.37068Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W. 6 2009 Long-time solutions of the Ostrovsky equation. Zbl 1194.35366Grimshaw, Roger; Helfrich, Karl 15 2008 Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory. Zbl 1155.35424El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. 15 2008 Rossby elevation waves in the presence of a critical layer. Zbl 1386.76049Caillol, P.; Grimshaw, R. H. 10 2008 Nonlinear free surface flows past a semi-infinite flat plate in water of finite depth. Zbl 1182.76484Maleewong, M.; Grimshaw, R. H. J. 4 2008 Rossby solitary waves in the presence of a critical layer. Zbl 1207.76044Caillol, Philippe; Grimshaw, Roger H. 3 2008 Gap-solitons in a three-layered stratified flow. Zbl 1231.76062Grimshaw, Roger; Christodoulides, Paul 2 2008 The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation. Zbl 1181.76040Grimshaw, 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 1122.76021El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M. 18 2007 Generation of solitary waves by transcritical flow over a step. Zbl 1141.76355Grimshaw, R. H. J.; Zhang, D.-H.; Chow, K. W. 10 2007 Internal solitary waves in a variable medium. Zbl 1121.76015Grimshaw, Roger 10 2007 Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. Zbl 1151.76399Akylas, T. R.; Grimshaw, R. H. J.; Clarke, S. R.; Tabaei, Ali 7 2007 Solitary waves in fluids. Zbl 1106.76007Grimshaw, R. H. J. (ed.) 5 2007 Solitary waves propagating over variable topography. Zbl 1310.76043Grimshaw, Roger 4 2007 Asymmetric internal solitary waves with a trapped core in deep fluids. Zbl 1182.76201Derzho, Oleg G.; Grimshaw, Roger 2 2007 Solitary wave solution for a non-integrable, variable coefficient nonlinear Schrödinger equation. Zbl 1118.35355Grimshaw, R.; Nakkeeran, K.; Poon, C. K.; Chow, K. W. 2 2007 Envelope solitary waves. Zbl 1316.76026Grimshaw, R. H. J. 1 2007 Unsteady undular bores in fully nonlinear shallow-water theory. Zbl 1185.76454El, 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 1091.35081Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R. 7 2006 Interactions of breathers and solitons in the extended Korteweg-de Vries equation. Zbl 1231.35196Chow, K. W.; Grimshaw, R. H. J.; Ding, E. 21 2005 Analytic model for a weakly dissipative shallow-water undular bore. Zbl 1144.37342El, 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 1145.76327El, G. A.; Grimshaw, R. H. J.; Kamchatnov, A. M. 8 2005 Generalized solitary waves and fronts in coupled Korteweg-de Vries systems. Zbl 1106.35079Fochesato, 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 1112.76317Maleewong, 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 1145.35446Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana; Ruderman, Michael; Erdélyi, Róbert 6 2005 Rossby waves on a shear flow with recirculation cores. Zbl 1145.76339Derzho, 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 1065.76021Maleewong, 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 1084.76004Grimshaw, Roger (ed.) 2 2005 Solitons in nonintegrable systems. Zbl 1144.37350Grimshaw, Roger H. J.; Ostrovsky, Lev A.; Pelinovsky, Dmitry E. 1 2005 Soliton dynamics in a strong periodic field: the Korteweg-de Vries framework. Zbl 1194.35367Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana 1 2005 Korteweg-de Vries equation. Zbl 1095.76013Grimshaw, Roger 1 2005 Interaction of two lump solitons described by the Kadomtsev-Petviashvili equation. Zbl 1163.74397Lu, Zhiming; Tian, Emily M.; Grimshaw, Roger 16 2004 Steady multipolar planar vortices with nonlinear critical layers. Zbl 1206.86006Caillol, P.; Grimshaw, R. 7 2004 Generation of secondary solitary waves in the variable-coefficient Korteweg-de Vries equation. Zbl 1141.35447Grimshaw, R. H. J.; Pudjaprasetya, S. R. 4 2004 Damping of large-amplitude solitary waves. Zbl 1163.74362Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana 12 2003 Solitary waves of a coupled Korteweg-de Vries system. Zbl 1013.35073Grimshaw, Roger; Iooss, Gerard 11 2003 The influence of modulational instability on energy exchange in coupled sine-Gordon equations. Zbl 1178.35330Griffiths, S. D.; Grimshaw, R. H. J.; Khusnutdinova, K. R. 3 2003 Generation of large-amplitude solitons in the extended Korteweg-de Vries equation. Zbl 1080.35532Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Slunyaev, Alexey 18 2002 Generation of undular bores in the shelves of slowly-varying solitary waves. Zbl 1080.76506El, G. A.; Grimshaw, R. H. J. 9 2002 Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model. Zbl 1184.76196Grimshaw, 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 1042.35066Grimshaw, Roger; Pelinovsky, Efim 5 2002 Nonlinear geostrophic adjustment in the presence of a boundary. Zbl 1063.76104Reznik, G. M.; Grimshaw, R. 4 2002 Dispersion management for solitons in a Korteweg-de Vries system. Zbl 1080.35522Clarke, Simon; Malomed, Boris A.; Grimshaw, Roger 3 2002 Solitary waves with recirculation zones in axisymmetric rotating flows. Zbl 1029.76008Derzho, Oleg; Grimshaw, Roger 2 2002 Nonlinear effects in wave scattering and generation. Flow interation with topography. Zbl 1187.76635Grimshaw, R. H. J. 1 2002 Long-wave instability in a three-layer stratified shear flow. Zbl 1152.76379Grimshaw, Roger; Skrynnikov, Yuri 1 2002 Integrable shallow-water equations and undular bores. Zbl 1152.76329El, G. A.; Grimshaw, R. H. J.; Pavlov, M. V. 22 2001 Wave group dynamics in weakly nonlinear long-wave models. Zbl 1006.76012Grimshaw, Roger; Pelinovsky, Dmitry; Pelinovsky, Efim; Talipova, Tatiana 15 2001 Short-wave instability in a three-layer stratified shear flow. Zbl 0987.76029Grimshaw, Roger; Christodoulides, Paul 3 2001 Ageostrophic dynamics of an intense localized vortex on a \(\beta\)-plane. Zbl 1046.76007Reznik, G. M.; Grimshaw, R. 2 2001 On the generation of solitons and breathers in the modified Korteweg-de Vries equation. Zbl 0970.35124Clarke, 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 1003.76015Reznik, G. M.; Grimshaw, R.; Benilov, E. S. 6 2000 Weakly nonlinear internal wave fronts trapped in contractions. Zbl 0956.76015Clarke, S. R.; Grimshaw, R. H. J. 5 2000 Models for long-wave instability due to a resonance between two waves. Zbl 0974.76030Grimshaw, R. 4 2000 Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity. Zbl 0933.35169Grimshaw, Roger; Polinovsky, Efim; Talipova, Tatjana 21 1999 Adjustment processes and radiating solitary waves in a regularised Ostrovsky equation. Zbl 0929.76025Grimshaw, R. H. J. 8 1999 Numerical simulations of internal solitary waves with vortex cores. Zbl 1051.76530Aigner, A.; Broutman, D.; Grimshaw, R. 3 1999 The effect of weak shear on finite-amplitude internal solitary waves. Zbl 0978.76015Clarke, S. R.; Grimshaw, R. H. J. 2 1999 Exact periodic steady solutions for nonlinear wave equations: a new approach. Zbl 0938.35129Grimshaw, Roger; Pavlov, Maxim 2 1999 Hamiltonian formulation for solitary waves propagating on a variable background. Zbl 0934.76011Grimshaw, R.; Pudjaprasetya, S. R. 2 1999 Passage of a wave pulse through a zero-dispersion point in the nonlinear Schrödinger equation. Zbl 1044.78508Clarke, 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 1136.76334Grimshaw, R. H. J.; He, J. -M.; Ostrovsky, L. A. 24 1998 Solitary wave transformation due to a change in polarity. Zbl 1020.35084Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatjana 6 1998 ...and 101 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,691 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. 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 Xin, Jie 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 Christodoulides, Paul 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 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 1,591 more Authors all top 5 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. 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