  The intersection of two ferromagnetic domain walls placed on the surface of
topological insulators provides a one-way beam splitter for domain-wall Dirac
fermions. Based on an analytic expression for a static two-soliton magnetic
texture we perform a systematic numerical study of the propagation of Dirac
wave packets along such intersections. A single-cone staggered-grid finite
difference lattice scheme is employed in the numerical analysis. It is shown
that the angle of intersection plays a decisive role in determining the
splitting ratio of the fermion beam. For a non-rectangular intersection, the
width and, to a lesser extent, the type of domain walls, e.g. Bloch or
N{\'e}el, determine the properties of the splitter. As the ratio between
domain-wall width and transverse localization length of the Dirac fermion is
increased its propagation behavior changes from quantum-mechanical (wave-like)
to classical ballistic (particle-like). An electric gate placed near the
intersection offers a dynamic external control knob for adjusting the splitting
ratio.
