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

✍ Scribed by Whitham, G. B.

• Book ID: 120114019
• Publisher: Cambridge University Press
• Year: 1965
• Tongue: English
• Weight: 202 KB
• Volume: 22
• Category: Article
• ISSN: 0022-1120
• DOI: 10.1017/S0022112065000745

✦ Synopsis

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.