Time domain scattering of scalar waves by two spheres in free-space

The formulation of time domain scattering of scalar waves by two scatterers of arbitrary shape is constructed using an equivalent of the T-matrix method formulated in the time domain. In the given solution, the positions of the scatterers are arbitrary, i.e., no simple special case of translation is chosen for them. The whole analysis is performed in the time domain requiring no inverse Fourier integrals to be evaluated. Scattering by two soft spheres in free-space is studied, as an example, in order to check the numerical accuracy, and demonstrate the utility of the expressions.