  In this paper, we present a numerical study of the properties of the flow
produced by the collision of a magnetized anisotropic pulsar wind with its
environment in binary system. We compare the impact of both the magnetic field
and the wind anisotropy to the benchmark case of a purely hydrodynamical (HD)
interaction of isotropic winds, which has been studied in detail by Bogovalov
et al. (2008). We consider the interaction in axisymmetric approximation, i.e.
the pulsar rotation axis is assumed to be oriented along the line between the
pulsar and the optical star and the effects related to the pulsar orbiting are
neglected. The impact of the magnetic field is studied for the case of weak
magnetization (with magnetization parameter $\sigma<0.1$), which is consistent
with conventional models of pulsar winds. The effects related to anisotropy in
pulsar winds are modeled assuming that the kinetic energy flux in a
non-magnetized pulsar wind is strongly anisotropic, with the minimum at the
pulsar rotation axis and the maximum in the perpendicular direction. We show
that, although both considered effects change the shape of the region occupied
by the terminated pulsar wind, their impact appears to be small. In particular,
for the magnetization of the pulsar wind below 0.1, the magnetic field pressure
remains well below the plasma pressure in the post-shock region. Thus, in the
case of interaction of a pulsar with the stellar wind environment (opposite to
the case of plerions, i.e. the pulsar interaction with the interstellar medium,
when the magnetic field becomes dynamically important independently on the wind
magnetization) the HD approach represents a feasible approximation for
numerical modelling.
