  A theoretical scheme for an experimental implementation involving bisolitonic
matter waves from an attractive Bose-Einstein condensate, is considered within
the framework of a non-perturbative approach to the associate Gross-Pitaevskii
equation. The model consists of a single condensate subjected to an expulsive
harmonic potential creating a double-condensate structure, and a gravitational
potential that induces atomic exchanges between the two overlapping post
condensates. Using a non-isospectral scattering transform method, exact
expressions for the bright-matter-wave bisolitons are found in terms of
double-lump envelopes with the co-propagating pulses displaying more or less
pronounced differences in their widths and tails depending on the mass of atoms
composing the condensate.
