Abstract
This note investigates the coupled Schrodinger system
iu(j) + Delta u(j) = - (Sigma(m)(k=1) a(jk)vertical bar u(k)vertical bar(p)) vertical bar u(j)vertical bar(p-2)u(j).
Indeed, beyond the mass-energy threshold given in Saanouni (Appl Anal, 2020. https://doi.org/10.1080/00036811.2020.1808201), a scattering versus finite time blow-up dichotomy is obtained in the mass super-critical and energy sub-critical regime. Moreover, one extends the previous work [18] to the non-radial case.