Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 300
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Adcock, Thomas A.A. and Taylor, Paul H. 2016. Non-linear evolution of uni-directional focussed wave-groups on a deep water: A comparison of models. Applied Ocean Research, Vol. 59, p. 147.


    Biondini, G. El, G.A. Hoefer, M.A. and Miller, P.D. 2016. Dispersive hydrodynamics: Preface. Physica D: Nonlinear Phenomena, Vol. 333, p. 1.


    Dutykh, Denys and Clamond, Didier 2016. Modified shallow water equations for significantly varying seabeds. Applied Mathematical Modelling,


    El, G.A. and Hoefer, M.A. 2016. Dispersive shock waves and modulation theory. Physica D: Nonlinear Phenomena, Vol. 333, p. 11.


    El, Gennady A. and Smyth, Noel F. 2016. Radiating dispersive shock waves in non-local optical media. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 472, Issue. 2187, p. 20150633.


    Gogoberidze, G 2016. On acoustic wave generation in uniform shear flow. Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue. 29, p. 295501.


    Hashemi, M. Reza Grilli, Stéphan T. and Neill, Simon P. 2016. A simplified method to estimate tidal current effects on the ocean wave power resource. Renewable Energy, Vol. 96, p. 257.


    Kalisch, Henrik Khorsand, Zahra and Mitsotakis, Dimitrios 2016. Mechanical balance laws for fully nonlinear and weakly dispersive water waves. Physica D: Nonlinear Phenomena, Vol. 333, p. 243.


    Kamchatnov, A.M. 2016. Whitham theory for perturbed Korteweg–de Vries equation. Physica D: Nonlinear Phenomena, Vol. 333, p. 99.


    Maltsev, A. Ya. 2016. On the canonical forms of the multi-dimensional averaged Poisson brackets. Journal of Mathematical Physics, Vol. 57, Issue. 5, p. 053501.


    Minzoni, A.A. and Smyth, Noel F. 2016. Modulation theory, dispersive shock waves and Gerald Beresford Whitham. Physica D: Nonlinear Phenomena, Vol. 333, p. 6.


    Nguyen, Lu Trong Khiem 2016. A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations. Communications in Nonlinear Science and Numerical Simulation, Vol. 36, p. 402.


    Omel’yanov, G. 2016. Propagation and interaction of solitons for nonintegrable equations. Russian Journal of Mathematical Physics, Vol. 23, Issue. 2, p. 225.


    Ratliff, Daniel J. and Bridges, Thomas J. 2016. Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics. Physica D: Nonlinear Phenomena, Vol. 333, p. 107.


    Sedletsky, Yu V 2016. Variational approach to the derivation of the Davey–Stewartson system. Fluid Dynamics Research, Vol. 48, Issue. 1, p. 015506.


    Smyth, Noel F. 2016. Dispersive shock waves in nematic liquid crystals. Physica D: Nonlinear Phenomena, Vol. 333, p. 301.


    Tovbis, Alexander and El, Gennady A. 2016. Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach. Physica D: Nonlinear Phenomena, Vol. 333, p. 171.


    Agrawal, Vaibhav and Dayal, Kaushik 2015. A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part I: Formulation and one-dimensional characterization. Journal of the Mechanics and Physics of Solids, Vol. 85, p. 270.


    Bridges, Thomas J. 2015. Breakdown of the Whitham Modulation Theory and the Emergence of Dispersion. Studies in Applied Mathematics, Vol. 135, Issue. 3, p. 277.


    Cao, Lei Hou, Yijun and Qi, Peng 2015. Altimeter significant wave height data assimilation in the South China Sea using Ensemble Optimal Interpolation. Chinese Journal of Oceanology and Limnology, Vol. 33, Issue. 5, p. 1309.


    ×

A general approach to linear and non-linear dispersive waves using a Lagrangian

  • G. B. Whitham (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112065000745
  • Published online: 01 March 2006
Abstract

The basic property of equations describing dispersive waves is the existence of solutions representing uniform wave trains. In this paper a general theory is given for non-uniform wave trains whose amplitude, wave-number, etc., vary slowly in space and time, the length and time scales of the variation in amplitude, wave-number, etc., being large compared to the wavelength and period. Dispersive equations may be derived from a variational principle with appropriate Lagrangian, and the whole theory is developed in terms of the Lagrangian. Boussinesq's equations for long water waves are used as a typical example in presenting the theory.

Copyright
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? *
×
MathJax