Projection Operator Method for Solving Coupled-Mode Equations: An Application to Separating Forward and Backward Scattered Acoustic Fields

摘要

Examined is the concept of a nonlocal effective interaction applied to scattering problems in underwater acoustics. A projection operator approach previously introduced in nuclear theory is employed to place the basic coupled mode integral equations into an alternate form. The dimension of the original coupled equations is reduced by half, to the dimension of the forward propagating modes, by a channel elimination process. The reduction in dimension occurs at the expense of the introduction of a nonlocal optical potential that couples the forward and backward propagating subspaces. A perturbation method leads to a multiple scattering representation of the effective interaction for the coupling. It is demonstrated that it is possible to generate a consistent methodology to separate the forward and backward propagating fields and to form a forward propagating field that includes perturbative corrections because of the coupling of the backward propagating field.