Revisiting asymptotic stability of solitons of nonlinear Schr\"odinger equations via refined profile method

Abstract

In this paper, we give an alternative proof for the asymptotic stability of solitons for nonlinear Schr\"odinger equations with internal modes. The novel idea is to use "refined profiles" developed by the authors for the analysis of small bound states. By this new strategy, we able to avoid the normal forms. Further, we can track the functions appearing in the Fermi Golden Rule hypothesis.