Abstract
AbstractA new source potential is constructed in the linearized theory of water waves. It is shown how this source potential may be used to reduce the problem of the reflexion and transmission of waves by a shelf of arbitrary profile to an integral equation. It is further shown that by suitably restricting the shelf profile, the Fred-holm theory is applicable to the integral equation so that in general a solution of the equation and hence of the problem, exists and is unique except possibly for certain discrete values of the parameters of the problem corresponding to trapping modes over the shelf.
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