An expansion theorem for two-dimensional elastic waves and its application

We prove an Atkinson-Wilcox-type expansion for two-dimensional elastic waves in this paper. The approach developed on the twodimensional Helmholtz equation will be applied in the proof. When the elastic fields are involved, the situation becomes much harder due to two wave solutions propagating at different phase velocities. In the last section, we give an application about the reconstruction of an obstacle from the scattering amplitude.