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In this note, we give an alternative proof of the theorem on solitonselection for small energy solutions of nonlinear Schr\"odinger equations (NLS)which we studied in Anal. PDE 8 (2015),  1289-1349 and more recently in Annals of PDE (2021) 7:16. As in in the latterpaper we use the notion of Refined Profile, with the difference that here we donot modify the modulation coordinates and we do not search for Darbouxcoordinates. This shortens considerably the proof.

A note on small data soliton selection for nonlinear Schr\"odinger equations with potential