Comments on a paper by Papadopoulos on the use of singular integrals in wave propagation problems

Abstract

In a recent paper Papadopoulos [1] ¹ claims to have obtained solutions to the problem of sound propagation from an impulsive point source in a semi-infinite elastic solid which differ in certain respects from solutions previously obtained by Pekeris [2], [3], and by Pekeris and Lifson [4]. The results of Papadopoulos are based on a singular integral source representation developed by him [5]. By tests based on simple special cases we show that, in a number of cases where Papadopoulos claims a result different from that of Pekeris, the results of Papadopoulos are unacceptable whereas the results of Pekeris are acceptable. Reasons for these errors in Papadopoulos's work are suggested. A number of other errors in the paper of Papadopoulos are also noted.