On modeling discontinuous media. One-dimensional approximations

Abstract
Distorted wave Born series are derived for the impedance equation [A−1(d/dx)A(d/dx)+k2]p=0, where A is a piecewise differentiable function. The first and second orders are given explicitly. They hold for impedances A, which include discontinuities, before and/or after perturbation, so that the problem could not be reduced to the Schrödinger one. The results are used for discussing homogenizations currently practiced in modeling discontinuous media.