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The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binaryBEC in an optical lattice (OL) and double well (DW) is studied using themean-field Gross-Pitaevskii equation. For both DW and OL, permanentself-trapping occurs in a window of the repulsive nonlinearity $g$ of the GPequation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities$g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials$\mu_{c1}<\mu<\mu_{c2}$ defining the band gap(s) of the periodic OL. Thepermanent self-trapped BEC in an OL usually represents a breathing oscillationof a stable stationary gap soliton. The permanent self-trapped BEC in a DW, onthe other hand, is a dynamically stabilized state without any stationarycounterpart. For a binary BEC with intraspecies nonlinearities outside thiswindow of nonlinearity, a permanent self trapping can be induced by tuning theinterspecies interaction such that the effective nonlinearities of thecomponents fall in the above window.

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction