Math 712. Topics in Mathematical Physics: Scattering for Nonlinear Klein Gordon
- Fall 20 -
Hans Lindblad
The course will be online in real time TuTh 10.30-11.45 at my zoom account.
The course will be about scattering for Nonlinear Klein Gordon, Nonlinear Schroedinger and Nonlinear wave equations with variable coefficients in one space dimension. The ultimate goal is to show stability of stationary solutions, so called kinks, as well as moving soliton solutions for certain nonlinear equations of mathematical physics.
Recently there has been a lot of activity in this area which uses some interesting math like spectral theory, estimates of Fourier Multipliers, twisted Fourier transform,... in order to study operators with variable coefficients.
In the past I have written papers with Avy Soffer and Terry Tao about this and recently also with Jonas Luhrman.
I will start by reviewing some of the earlier works. The main focus will be to go over two recent papers:
Chen and Pusateri
and Germain and Pusateri
as well as the background material needed to understand these papers.