  The quasi-stationary method for black hole binary inspiral is an
approximation for studying strong field effects while suppressing radiation
reaction. In this paper we use a nonlinear scalar field toy model (i) to
explain the underlying method of approximating binary motion by periodic orbits
with radiation; (ii) to show how the fields in such a model are found by the
solution of a boundary value problem; (iii) to demonstrate how a good
approximation to the outgoing radiation can be found by finding fields with a
balance of ingoing and outgoing radiation (a generalization of standing waves).
