To account for caustic phenomena, Kamill and his pupil Arkady M. Aizenberg introduced the edge-wave superposition method (EWSM) for 2D forward problems in 1980 and the tip-wave superposition method (TWSM) for 3D forward problems in 1985. To account for reflection/transmission at curved interfaces, Kamill introduced new rigorous reflection/transmission operators at curved contacts of acoustic media (with coauthors A. M. Aizenberg, Hans B. Helle, and Jan Pajchel, in Wave Motion, 2004, 39, 77-92; 2005, 41, 293-305). Unfortunately, Kamill did not have enough time to solve a problem of diffraction on smooth parts of curved interfaces and left that to his followers.
