On a Singular Integrodifferential Equation arising from a Linearised Free Surface Problem

Details On a Singular Integrodifferential Equation arising from a Linearised Free Surface Problem On a Singular Integrodifferential Equation arising from a Linearised Free Surface Problem

2005-12-14

arxiv.org/abs/math/0512303v1

Mathematics

Classical Analysis and ODEs

8 pages, 1 figure, draft

Scientific paper

A problem of linear surface waves discussed by Forbes(1984) initially gave rise to a singular integrodifferential equation over the real line. We have been able to transform this integrodifferential equation into a linear second order differential equation whose solution has been found explicitly in terms of the sine and cosine integral functions. Furthermore, we have been able to recover known results of physical interest using more simple techniques.

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