%0 Report %D 2018 %T Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis %A Alessandro Michelangeli %A Giuseppe Pitton %X We present a numerical study of the two-dimensional 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. %G en %U http://preprints.sissa.it/handle/1963/35323 %1 35633 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-20T06:04:10Z No. of bitstreams: 1 SISSA_preprint_35-2018-MATE.pdf: 2536075 bytes, checksum: 323dca7431103028ecadfc71c052f4ed (MD5) %0 Report %D 2016 %T Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics %A Alessandro Michelangeli %A Giuseppe Pitton %X 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35266 %1 35572 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:09:24Z No. of bitstreams: 1 SISSA_preprint_63-2016-MATE_Michelangeli-Pitton-2016.pdf: 6158349 bytes, checksum: ab11de2762ff510e6833474d0688a8b4 (MD5)