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Analytic solution of the linearized shallow-water wave equations for certain continuous depth variations

Published online by Cambridge University Press:  17 February 2009

D. L. Clements  and
C. Rogers
D. L. Clements
Affiliation:
Department of Applied Mathematics, University of Adelaide, Australia
C. Rogers
Affiliation:
S.L.I.S. University of Western Ontario, London, Canada.
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Abstract

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The linear long-wave equations with (and without) small ground motion are considered. The governing equations are represented in a matrix from and transformations are sought which reduce the system to (for example) a form associated with the conventional wave equation. Integration of the system is then immediate. It is shown that such a reduction may be acheived provided the variation in water depth is specified by certain multi-parameter forms.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 1 , June 1975 , pp. 81 - 94
Copyright
Copyright © Australian Mathematical Society 1975

References

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