Mathematics

We present a comprehensive discussion of the mathematical framework
for binary Bose-Einstein condensates and for the rigorous derivation of their effective
dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations.
We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii
systems in a wide range of relevant regimes of population ratios and intra-species and
inter-species interactions. Our numerical method is based on a Fourier collocation
scheme in space combined with a fourth order integrating factor scheme in time.