A two-way parabolic equation that accounts for multiple scattering

A two-way parabolic equation that accounts for multiple scattering is derived and tested. A range-dependent medium is divided into a sequence of range-independent regions. The field is decomposed into outgoing and incoming fields in each region. The conditions between vertical interfaces are implemented using rational approximations for the square root of an operator. Rational approximations are also used to relate fields between neighboring interfaces. An iteration scheme is used to solve for the outgoing and incoming fields at the vertical interfaces. The approach is useful for solving problems involving scattering from waveguide features and compact objects.