  Recent neutron scattering studies revealed the three dimensional character of
the magnetism in the iron pnictides and a strong anisotropy between the
exchange perpendicular and parallel to the spin stripes. We extend studies of
the J1-J2-Jc Heisenberg model with S = 1 using self-consistent spin-wave
theory. A discussion of two scenarios for the instability of the columnar phase
is provided. The relevance of a biquadratic exchange term between in-plane
nearest neighbors is discussed. We introduce mean-field decouplings for
biquadratic terms using the Dyson-Maleev and the Schwinger boson
representation. Remarkably their respective mean-field theories do not lead to
the same results, even at zero temperature. They are gauged in the N'eel phase
in comparison to exact diagonalization and series expansion. The J1-J2-Jc model
is analyzed under the influence of the biquadratic exchange Jbq and a detailed
description of the staggered magnetization and of the magnetic excitations is
given. The biquadratic exchange increases the renormalization of the in-plane
exchange constants which enhances the anisotropy between the exchange parallel
and perpendicular to the spin stripes. Applying the model to iron pnictides, it
is possible to reproduce the spin-wave dispersion for CaFe2As2 in the direction
perpendicular to the spin stripes and perpendicular to the planes.
Discrepancies remain in the direction parallel to the spin stripes which can be
resolved by passing from S = 1 to S = 2. In addition, results for the dynamical
structure factor within the self-consistent spin-wave theory are provided.
