The Bremmer series for a multi-dimensional acoustic scattering problem

The Bremmer series is used to reduce a complex scattering problem to a sequence of simpler single-scattering problems. In the Bremmer series, the wave equation is first decomposed into a coupled system of one-way wave equations. The system is then decoupled into a sequence of one-way wave equations with a fixed-point iteration. In this paper, a left-symbol representation of the decomposition operator and the vertical-propagation operator are used. Time-domain convergence of the Bremmer series is shown for a set of dispersive medium models. The non-dispersive case is treated with an approximation procedure.