Scattering for systems of N weakly coupled NLS equations on ℝd × ℳk in non-isotropic Sobolev fractional spaces.

We study scattering properties in non-isotropic Sobolev fractional spaces for small data solutions to the following system of N ≥ 2, nonlinear Schrödinger equations (NLS) having mass-supercritical power-type nonlinearity and posed on product spaces ℝd × ℳk, for d, k ≥ 1 and ℳk any k-dimensional compact Riemaniann manifold. [ABSTRACT FROM AUTHOR]