Dynamics of subcritical threshold solutions for energy-critical NLS

In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on Rᵈ (d≥ 5) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in {DM} for $d=3,4,5$ and later by D. Li and X. Zhang in {LZ} for d ≥ 6. We generalize the conclusion for the subcritical threshold solutions by removing the radial assumption for d≥ 5. A key step is to show exponential convergence to the ground state $W(x)$ up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate are applied.