  We study solitons in the condensate trapped in a double-well potential with
far-separated wells, when the s-wave scattering length has different signs in
the two parts of the condensate. By employing the coupled-mode approximation it
is shown that there are unusual stable bright solitons in the condensate, with
the larger share of atoms being gathered in the repulsive part. Such unusual
solitons derive their stability from the quantum tunneling and correspond to
the strong coupling between the parts of the condensate. The ground state of
the system, however, corresponds to weak coupling between the condensate parts,
with the larger share of atoms being gathered in the attractive part of the
condensate.
