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

  • G. B. Whitham (a1)

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.

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Korteweg, D. J. & de Vries, G.1895Phil. Mag.39, 422.

Rüssman, H.1961Arch. Rat. Mech. Anal.8, 353.

Whitham, G. B.1965Proc. Roy. Soc. A, 283, 238.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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