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Journal of Nonlinear Mathematical Physics Volume 9, 2002 - Issue sup1: Recent Advances in Integrable Systems
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Original Articles

Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations

Yi A Li Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, 07030, U.S. E-mail: [email protected]
Pages 99-105 | Received 30 May 2001, Accepted 15 Jul 2001, Published online: 21 Jan 2013

Citations (26)

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DELIA IONESCU-KRUSE. (2012) VARIATIONAL DERIVATION OF THE GREEN–NAGHDI SHALLOW-WATER EQUATIONS. Journal of Nonlinear Mathematical Physics 19:sup1, pages 1-12.
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Articles from other publishers (25)

Lili Fan, Hongjun Gao & Haochen Li. (2022) On the Geophysical Green-Naghdi System. Journal of Nonlinear Science 32:2.
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Vincent Duchêne & Christian Klein. (2022) Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart. Discrete and Continuous Dynamical Systems - B 27:10, pages 5905.
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Vincent Duchêne, Dag Nilsson & Erik Wahlén. (2017) Solitary Wave Solutions to a Class of Modified Green–Naghdi Systems. Journal of Mathematical Fluid Mechanics 20:3, pages 1059-1091.
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Vincent Duchêne & Samer Israwi. (2018) Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems. Annales Mathématiques Blaise Pascal 25:1, pages 21-74.
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Alexei F. Cheviakov. (2018) Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model. Physica D: Nonlinear Phenomena 370, pages 14-28.
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J.P.A. Pitt, C. Zoppou & S.G. Roberts. (2018) Behaviour of the Serre equations in the presence of steep gradients revisited. Wave Motion 76, pages 61-77.
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Bo Jiang & Qinsheng Bi. (2017) Classification of traveling wave solutions to the Green–Naghdi model. Wave Motion 73, pages 45-56.
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D. Mitsotakis, C. Synolakis & M. McGuinness. (2017) A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system. International Journal for Numerical Methods in Fluids 83:10, pages 755-778.
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D. C. Antonopoulos, V. A. Dougalis & D. E. Mitsotakis. (2017) Error Estimates for Galerkin Approximations of the Serre Equations. SIAM Journal on Numerical Analysis 55:2, pages 841-868.
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V. Duchêne, S. Israwi & R. Talhouk. (2016) A New Class of Two-Layer Green-Naghdi Systems with Improved Frequency Dispersion. Studies in Applied Mathematics 137:3, pages 356-415.
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Henrik Kalisch, Zahra Khorsand & Dimitrios Mitsotakis. (2016) Mechanical balance laws for fully nonlinear and weakly dispersive water waves. Physica D: Nonlinear Phenomena 333, pages 243-253.
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Dena Kazerani. (2016) Global existence for small data of the viscous Green–Naghdi type equations. Journal of Differential Equations 261:1, pages 762-796.
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Yoshimasa Matsuno. (2016) Hamiltonian structure for two-dimensional extended Green–Naghdi equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472:2190, pages 20160127.
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Didier Clamond & Denys Dutykh. 2016. New Approaches to Nonlinear Waves. New Approaches to Nonlinear Waves 197 210 .
Delia Ionescu-Kruse. (2015) A new two-component system modelling shallow-water waves. Quarterly of Applied Mathematics 73:2, pages 331-346.
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Dimitrios Mitsotakis, Boaz Ilan & Denys Dutykh. (2014) On the Galerkin/Finite-Element Method for the Serre Equations. Journal of Scientific Computing 61:1, pages 166-195.
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Angel Duran, Denys Dutykh & Dimitrios Mitsotakis. (2013) On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations. Studies in Applied Mathematics 131:4, pages 359-388.
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DENYS DUTYKH, DIDIER CLAMOND, PAUL MILEWSKI & DIMITRIOS MITSOTAKIS. (2013) Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. European Journal of Applied Mathematics 24:5, pages 761-787.
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Francesco CarboneDenys DutykhJohn M. DudleyFrédéric Dias. (2013) Extreme wave runup on a vertical cliff. Geophysical Research Letters 40:12, pages 3138-3143.
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SHENGFU DENG, BOLING GUO & TINGCHUN WANG. (2013) TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM. International Journal of Bifurcation and Chaos 23:05, pages 1350087.
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Didier Clamond & Denys Dutykh. (2012) Practical use of variational principles for modeling water waves. Physica D: Nonlinear Phenomena 241:1, pages 25-36.
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John D. Carter & Rodrigo Cienfuegos. (2011) The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations. European Journal of Mechanics - B/Fluids 30:3, pages 259-268.
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SHENGFU DENG, BOLING GUO & TINGCHUN WANG. (2011) SOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEM. International Journal of Bifurcation and Chaos 21:02, pages 575-585.
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J R Percival, C J Cotter & D D Holm. (2008) A Euler–Poincaré framework for the multilayer Green–Nagdhi equations. Journal of Physics A: Mathematical and Theoretical 41:34, pages 344018.
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V. A. Dougalis, A. Durán, M. A. López-Marcos & D. E. Mitsotakis. (2007) A Numerical Study of the Stability of Solitary Waves of the Bona–Smith Family of Boussinesq Systems. Journal of Nonlinear Science 17:6, pages 569-607.
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