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

Published online by Cambridge University Press:  28 March 2006

G. B. Whitham
G. B. Whitham
Affiliation:
California Institute of Technology
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 22 , Issue 2 , June 1965 , pp. 273 - 283
Copyright
© 1965 Cambridge University Press

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References

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