When we analyze the reflection phenomenon for the elastic wave, the one of the most complicated and interesting problems is to study the mode conversion case. For the elastic wave, there are waves of different modes and a remarkable phenomenon called "mode-conversion'' which causes serious difficulties. In this paper, by considering the non back-scattering case, we examine the singularities of the scattering kernel for the elastic wave equation with transverse incident waves and derive a new result about the singularities of the scattering kernel.
"On the analysis of the scattering problem for the elastic wave in the case of the transverse incident wave." Proc. Japan Acad. Ser. A Math. Sci. 85 (9) 138 - 142, November 2009. https://doi.org/10.3792/pjaa.85.138