Edge Green's functions on branched surfaces. Formulation of the problem for finding unknown constants

A. V. Shanin

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 220-244

Résumé

Current work is the continuation of [1], where the coordinate and the spectral equations were derived for finding the edge Green's functions on a branched surface having branch points of second order. The coefficients of the equations contain unknown numerical parameters. To find these parameters one has to formulate a set of restrictions, which should be obeyed by the solutions of the equations. After that, the unknown constants can be found numerically. Current work is dedicated to the formulation of the problem for finding the unknown constants. The consideration is held for the branched surface corresponding to the problem of diffraction by an angle reflector with a gap. As a result of using a subtle property of the spectral equation, namely a symmetry corresponding to the reciprocity, it becomes possible to construct a set of restrictions, in which the number of restrictions is equal to the number of unknown parameters. Bibl. – 2 titles, fig. – 6.