This paper deals with the frequency domain wave equation for media with variable mass density and wave speed. We transform this wave equation into an equivalent set of two coupled integral equations for the pressure and pressure gradient fields. Then we discuss monolithic and stabilized splitting solutions strategies. By splitting the coupled integral equations in multi-parameter scattering theory one can potentially employ existing solvers and preconditioners for the single-parameter scattering cases. Also, the splitting solution strategy allows for better convergence control and memory management.