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Solitary wave solutions for a model of the two-way propagation of water waves in a channel

Published online by Cambridge University Press:  24 October 2008

J. F. Toland
J. F. Toland
Affiliation:
University College, London
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Extract

Bona and Smith (6) have suggested that the coupled system of equations

has the same formal justification as other Boussinesq-type models for the two-way propagation of one-dimensional water waves of small but finite amplitude in a channel with a flat bottom. The variables u and η represent the velocity and elevation of the free surface, respectively. Using the energy invariant

they show that for a restricted, but nevertheless physically relevant, class of initial data, the system (1·1) has solutions which exist for all time, and that in such circumstances the wave height is bounded solely in terms of the initial data.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 343 - 360
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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