Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 22
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Seadawy, A.R. El-Kalaawy, O.H. and Aldenari, R.B. 2016. Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability. Applied Mathematics and Computation, Vol. 280, p. 57.

    Shimizu, Chika and Shōji, Mayumi 2012. Appearance and disappearance of non-symmetric progressive capillary–gravity waves of deep water. Japan Journal of Industrial and Applied Mathematics, Vol. 29, Issue. 2, p. 331.

    Belibassakis, K.A. and Athanassoulis, G.A. 2011. A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions. Coastal Engineering, Vol. 58, Issue. 4, p. 337.

    Ehrnstrom, M. Holden, H. and Raynaud, X. 2009. Symmetric Waves Are Traveling Waves. International Mathematics Research Notices,

    Gao, Liang Ma, Wen-Xiu and Xu, Wei 2009. Travelling wave solutions to Zufiria’s higher-order Boussinesq type equations. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 12, p. e711.

    Grujić, Zoran and Kalisch, Henrik 2009. Gevrey regularity for a class of water-wave models. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 3-4, p. 1160.

    Aider, Rabah and Debiane, Mohammed 2006. A method for the calculation of nonsymmetric steady periodic capillary–gravity waves on water of arbitrary uniform depth. Comptes Rendus Mécanique, Vol. 334, Issue. 6, p. 387.

    Bridges, T.J. and Fan, E.G. 2004. Solitary waves, periodic waves, and a stability analysis for Zufiria's higher-order Boussinesq model for shallow water waves. Physics Letters A, Vol. 326, Issue. 5-6, p. 381.

    Craig, Walter and Nicholls, David P. 2002. Traveling gravity water waves in two and three dimensions. European Journal of Mechanics - B/Fluids, Vol. 21, Issue. 6, p. 615.

    Nicholls, David P. 1998. Traveling Water Waves: Spectral Continuation Methods with Parallel Implementation. Journal of Computational Physics, Vol. 143, Issue. 1, p. 224.

    Benjamin, T. Brooke 1995. Verification of the Benjamin–Lighthill conjecture about steady water waves. Journal of Fluid Mechanics, Vol. 295, Issue. -1, p. 337.

    Bhattacharyya, S.K. 1995. On two solutions of fifth order Stokes waves. Applied Ocean Research, Vol. 17, Issue. 1, p. 63.

    Bridges, T. J. 1994. Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference. Journal of Nonlinear Science, Vol. 4, Issue. 1, p. 221.

    Craig, Walter and Groves, Mark D. 1994. Hamiltonian long-wave approximations to the water-wave problem. Wave Motion, Vol. 19, Issue. 4, p. 367.

    Baesens, C. and Mackay, R. S. 1992. Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family. Journal of Fluid Mechanics, Vol. 241, Issue. -1, p. 333.

    Bridges, Thomas J. 1992. Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrödinger equations. Physica D: Nonlinear Phenomena, Vol. 57, Issue. 3-4, p. 375.

    Aston, P. J. 1991. Analysis and Computation of Symmetry-Breaking Bifurcation and Scaling Laws Using Group-Theoretic Methods. SIAM Journal on Mathematical Analysis, Vol. 22, Issue. 1, p. 181.

    1989. Hydrodynamics of Coastal Zones.

    Longuet-Higgins, M. S. 1988. Lagrangian moments and mass transport in Stokes waves Part 2. Water of finite depth. Journal of Fluid Mechanics, Vol. 186, Issue. -1, p. 321.

    Pullin, D. I. and Grimshaw, R. H. J. 1988. Finite-amplitude solitary waves at the interface between two homogeneous fluids. Physics of Fluids, Vol. 31, Issue. 12, p. 3550.

  • Journal of Fluid Mechanics, Volume 180
  • July 1987, pp. 371-385

Weakly nonlinear non-symmetric gravity waves on water of finite depth

  • J. A. Zufiria (a1)
  • DOI:
  • Published online: 01 April 2006

A weakly nonlinear Hamiltonian model for two-dimensional irrotational waves on water of finite depth is developed. The truncated model is used to study families of periodic travelling waves of permanent form. It is shown that non-symmetric periodic waves exist, which appear via spontaneous symmetry-breaking bifurcations from symmetric waves.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *