Publisher's Synopsis
Excerpt from The Solitary Wave and Periodic Waves in Shallow Water
Numbers in square brackets refer to the bibliography at the end of the article.
The theory given by Boussinesq involves a number of phys ical assumptions in addition to those of the basic hydro dynamical theory; it also leads to a differential equa tion for the wave profile. Both of these methods assume that the depth of the water is small compared to some horizontal dimension, and they might be interpreted as developments of the whole problem in powers of the ratio of the depth to some horizontal dimension, such as wave length. However, because these procedures are so unsys tematic, it is not clear that they are equivalent to such developments, nor to what order of approximation the so lutions obtained are valid. The method of proceeding to higher approximations is also obscure.
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