The APDE seminar on Monday, 4/22, will be given by Dongxiao Yu (Berkeley) in-person in **Evans 740,** and will also be broadcasted online via Zoom from **4:10pm to 5:00pm PST**. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

**Title:** Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms

**Abstract:** I will present a joint work with Herbert Koch on the asymptotic stability of the sine-Gordon kinks under small perturbations in weighted Sobolev norms. Our main tool is the Bäcklund transform which reduces the study of the asymptotic stability of the kinks to the study of the asymptotic decay of solutions near zero. I will also compare our work with some previous work on the asymptotic stability of the sine-Gordon kinks.