**Figure 1.** Density profiles for repulsive binary spatially inhomogeneous strengths: (a) γ_{1} = 1, (b) γ_{1} = 100, (c) γ_{1} = 500, (d) γ_{1} = 1000 with the potential (5).

**Abstract**

We study the impact of collisionally inhomogeneous binary and three-body interaction on Bose–Einstein condensates (BECs) of a dilute gas in a bichromatic optical lattice. We observe that the localized matter wave density which decreases after the introduction of repulsive spatially inhomogeneous binary interaction can be sustained by the addition of constant attractive binary strength in equal amounts. If the balance between repulsive spatially inhomogeneous binary interaction and constant attractive interaction is disturbed, the condensates collapse. Reversal of interaction sign ensures the longevity of BECs. Any imbalance between attractive spatially inhomogeneous interaction and constant repulsive interaction either results in the collapse of BECs or in the occupation of the condensates at multiple sites on either side. The introduction of a weak three-body interaction in phase with the binary interaction increases the extent of the instability of BECs. Reversing the sign of spatially inhomogeneous and constant interaction enhances the stability of BECs.