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Contributions to the Theory of Waves in Non-linear Dispersive Systems

In: Hyperbolic Equations and Waves

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  • M. J. Lighthill

Abstract

This paper makes contributions to the general theory of wave propagation in conservative systems under conditions when the proportional change in amplitude or wavenumber over a distance of one wavelength is very small. For linear systems, such propagation is governed by the well-known theory of group velocity; there is “frequency dispersion”, in the sense that energy in components of different frequency is propagated at different group velocities. For non-linear systems without frequency dispersion, e.g. acoustic systems, a different, but also well-known, modification of the waveform occurs. It may be called “amplitude dispersion”, in that different values of an amplitude variable like the pressure are propagated at different speeds.

Suggested Citation

  • M. J. Lighthill, 1970. "Contributions to the Theory of Waves in Non-linear Dispersive Systems," Springer Books, in: M. Froissart (ed.), Hyperbolic Equations and Waves, pages 173-210, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-87025-5_17
    DOI: 10.1007/978-3-642-87025-5_17
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