  We study the localization transition in a spin-orbit (SO) coupled binary
Bose-Einstein condensates (BECs) with collisional inhomogeneous interaction
trapped in a one-dimensional quasiperiodic potential. Our numerical analysis
shows that the competition between the quasiperiodic disorder and inhomogeneous
interaction leads to a reentrant localization transition as the interaction
strength is tuned from attractive to repulsive in nature. Further, we analyse
the combined effect of the SO and Rabi coupling strengths on the localization
transition for different interaction strengths and obtain signatures of
reentrant localization transition as function of SO coupling in the regime of
weak interactions. We complement our numerical observation with the analytical
model using the variational approach. At the end we show how the reentrant
localization is manifested in the quench dynamics of the condensate. Our study
provides an indirect approach to achieve localization transition without tuning
the quasiperiodic potential strength, rather by tuning the inhomogeneous
interaction.
