Dynamics of bisolitonic matter waves in a Bose-Einstein condensate subjected to an atomic beam splitter and gravity

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.