  We show that a vector matter-wave soliton in Bose-Einstein condensate loaded
into an optical lattice can escape from a trap formed by a parabolic potential,
resembling a Hawking emission. The particle-antiparticle pair is emulated by a
low-amplitude bright-bright soliton in two-component Bose-Einstein condensate
with effective masses of opposite signs. It is shown that the parabolic
potential leads to a spatial separation of BEC components. One component with
chemical potential in a semi-infinite gap exerts periodical oscillations, while
the other BEC component, with negative effective mass, escapes from the trap.
The mechanism of atoms transfer from one BEC component to another by spatially
periodic linear coupling term is discussed.
