The pattern equation method based on the Wilcox representation

Remarks on the study “The pattern equation method based on the Wilcox representation“ by A.G. Kyurkchan and N.I. Smirnova

“…We note in conclusion that the idea of representing in [1] the sought scattered field within the framework of the PEM with the use of the Atkinson-Wilcox expansion is not new. This expansion is applied by another author in [8], where an approach similar to the PEM is described.…”

“…In study [1], the authors characterize the pattern equation method (PEM) and note that certain aspects of the PEM were applied in [2][3][4]. 1 This characterization does not raise objections to the analysis presented in studies [3] and [4], which were published substantially later than [5], the first study on the PEM. The presence of a reference to study [2], which was ignored by the author of the PEM in his previous studies on this method, can be regarded favorably.…”

“…This expansion is applied by another author in [8], where an approach similar to the PEM is described. Study [8] is not cited in [1], while the author of [8] considers the vector problem of electromagnetic scattering; this problem is more complicated than the scalar problem analyzed in [1], where the possibility of generalization of the approach from [1] to vector problems is only supposed. In addition, numerical results are presented in [8] for a cubic scatterer, rather than for the trivial case of a sphere as in [1].…”