## Mathematical Physics and Harmonic Analysis Seminar

**Date:** November 22, 2019

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Jonas Luhrmann, Texas A&M University

**Title:** *Stability of kinks and dispersive decay of Klein-Gordon waves*

**Abstract:** Kinks are particle-like solitons that arise in nonlinear scalar field theories in one space dimension. In this talk I will explain how the study of the asymptotic stability of kinks centers on the long-time behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient nonlinearities. Then I will present a new result on sharp decay estimates and asymptotics for small solutions to variable coefficient cubic nonlinear Klein-Gordon equations. If time permits, I will also discuss work in progress on the variable coefficient quadratic case, which exhibits a striking resonant interaction between the spatial oscillations of the variable coefficient and the temporal oscillations of the solutions. This is joint work with Hans Lindblad and Avy Soffer.