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On a singular integral equation with logarithmic and Cauchy kernel. (English) Zbl 0880.45003

Summary: A singular integral equation (SIE) of the first kind with a combination of logarithmic and Cauchy type kernel is solved in closed form. This SIE arises in linear water wave theory.

MSC:

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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