New Analytical Solution for Nonlinear Shallow Water-Wave Equations

New Analytical Solution for Nonlinear Shallow Water-Wave Equations We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-averaged velocity, compare with existing solutions, and observe perfect agreement with substantially less computational effort. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure and Applied Geophysics Springer Journals

New Analytical Solution for Nonlinear Shallow Water-Wave Equations

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Earth Sciences; Geophysics/Geodesy
ISSN
0033-4553
eISSN
1420-9136
D.O.I.
10.1007/s00024-017-1508-z
Publisher site
See Article on Publisher Site

Abstract

We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-averaged velocity, compare with existing solutions, and observe perfect agreement with substantially less computational effort.

Journal

Pure and Applied GeophysicsSpringer Journals

Published: Mar 20, 2017

References

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