Yongming Li: Asymptotic stability of solitary waves for the 1D cubic NLS under even perturbations

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November 04, 2024 1:15 pm - 2:05 pm ET
Seminars,
Analysis Seminar
LGRT 1685

Yongming Li

Texas A&M University

Asymptotic stability of solitary waves for the 1D cubic NLS under even perturbations

I will present an overview for our proof of the asymptotic stability of solitary waves for the  1D cubic NLS under even perturbations, which is based on a combination of modulation techniques, distorted Fourier transform, and a space-time resonances approach. The main challenges are the threshold resonances of the linearized operator and the resulting slow local decay of the Schrödinger waves. Remarkable null structures in the evolution equation for the radiation term as well as in the modulation equations play an important role in the proof. This is joint work with Jonas Lührmann (Texas A&M University).