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The Quarterly Journal of Mechanics and Applied Mathematics 2005 58(2):289-308; doi:10.1093/qjmamj/hbi015
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Q. Jl Mech. Appl. Math. (2005) 58 (2), 289–308 © Oxford University Press 2005; all rights reserved.

Coordinate equations for a problem on a sphere with a cut associated with diffraction by an ideal quarter-plane

A. V. Shanin *

( Department of Physics, Moscow State University, Leninskie Gory, Moscow 119992, Russia )

In our prior work, a set of modified Smyshlyaev formulae was derived for the problem of diffraction by a Dirichlet flat cone (quarter-plane). The problem was reduced to finding the so-called edge Green's functions on a unit sphere. Here we explain how these edge Green's functions can be calculated. The new method proposed for this can be considered as a generalization of the method of separation of variables, since it reduces the partial differential equation to a system of ordinary differential equations in some sense. We demonstrate also a numerical application of the new method.

Received 18 February 2004. Revise 28 January 2005.

* <andrey_shanin{at}mail.ru>


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