Toronto, December 2 - 5, 2022
The starting point for the analysis of all these coherent structures is the linearization of the equations in their vicinity. This naturally leads to study nonlinear evolution equations of wave/dispersive-type with large potentials. In this talk we will give an introduction to this class of problems, and present some recent results with applications to the stability of kinks and Solitons, and to the phenomenon of “Radiation Damping”. Our general approach is based on the use of the distorted Fourier transform, that is, the Fourier transform adapted to a Schr\"odinger operator, and the development of multilinear Harmonic Analysis in this setting.
This talk is based on joint works with P. Germain (Imperial), F. Rousset (Paris-Saclay Orsay), A. Soffer (Rutgers), G. Chen (Georgia Tech), T. L\'eger (Princeton), Z. Zhang (NYU), A. Kairzhan (U of Toronto).