  We consider a matter wave bright soliton interferometer composed of a
harmonic potential trap with a Rosen--Morse barrier at its center on which an
incident soliton collides and splits into two solitons. These two solitons
recombine after a dipole oscillation in the trap at the position of the
barrier. We focus on the characterization of the splitting process in the case
in which the reflected and transmitted solitons have the same number of atoms.
We obtain that the velocity of the split solitons strongly depends on the
nonlinearity and on the width of the barrier and that the reflected soliton is
in general slower than the transmitted one. Also, we study the phase difference
acquired between the two solitons during the splitting and we fit
semi-analytically the main dependences with the velocity of the incident
soliton, the nonlinearity and the width of the barrier. The implementation of
the full interferometer sequence is tested by means of the phase imprinting
method.
