  A major challenge in the theoretical modeling of double-slit interferometry
involving matter-wave fields is the appropriate waveform to be assigned to this
field. While all the studies carried out to date on this issue deal with
variational fields, experiments suggest that the optical field is generated by
splitting a single-hump Bose-Einstein condensate into two spatially and
temporally entangled pulses indicating the possibility of fully controlling the
subsequent motion of the two output pulses. To probe the consistency of
variational and exact soliton solutions to the field equation, we solve the
Gross-Pitaevskii equation with an optical potential barrier assumed to act as a
beam splitter, while including gravity. The exact solution is compared with the
two most common variational wavefunctions, namely, the Hermite-Gaussian and
super-sech modes. From numerical simulations, evidence is given of the exact
solution as being the most appropriate matter-wave structure that provides a
coherent description of the generation and spatio-temporal evolution of
matter-wave optical fields in a hypothetical implementation of double-slit atom
interferometry
