Escape of a vector matter-wave soliton from a parabolic trap

We show that a vector matter-wave soliton in a Bose-Einstein condensate (BEC) 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 a two-component BEC 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 atom transfer from one BEC component to another by spatially periodic linear coupling term is also discussed.