Difference between revisions of "Helmholtz's Equation"
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satisfy Helmholtz's equation. This means that many asymptotic results in linear water waves can be | satisfy Helmholtz's equation. This means that many asymptotic results in linear water waves can be | ||
derived from results in acoustic or electromagnetic scattering. | derived from results in acoustic or electromagnetic scattering. | ||
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| + | [http://en.wikipedia.org/wiki/Helmholtz_equation External link] | ||
[[Category:Linear Water-Wave Theory]] | [[Category:Linear Water-Wave Theory]] | ||
Revision as of 01:52, 7 July 2006
This is a very well known equation given by
[math]\displaystyle{ \nabla^2 \phi - k^2 = 0 }[/math].
It applies to a wide variety of situations such as electromagnetics and acoustics. In water waves it arises when we Remove The Depth Dependence. Often there is then a cross over from the study of water waves to the study of scattering problems more generally. Also, if we perform a Cylindrical Eigenfunction Expansion we find that the modes all decay rapidly as distance goes to infinity except the solutions which satisfy Helmholtz's equation. This means that many asymptotic results in linear water waves can be derived from results in acoustic or electromagnetic scattering.
