Lecture Course (250 072 VO):
Time: Tuesday, 13:30 - 15:00 h
Start: April 13, 2021
End: May 25, 2021
Abstract: This class will provide an overview of the subject of soliton stability in dimension one. Solitons are fundamental objects in nonlinear wave equations, or nonlinear physics in general, and the question of their stability is the first one to ask. Much progress has been made since the 70's, but much remains to be done in this exciting field! The mathematical tools which come into play are nonlinear functional analysis and Fourier analysis.
Content of the lecture course (tentative):
1. The Physics and the structure of the equations
2. The distorted Fourier transform
3. Linear estimates: dispersive and Strichartz estimates
4. Orbital stability
5. Asymptotic stability & modulation
6. Asymptotic stability & resonances
7. Internal modes and Bremsstrahlung
Aim of the course: Provide an overview of the subject of soliton stability in dimension one
Due to the current COVID situation the course will be held online via zoom. Zoom coordinates will be available on request.
Soliton stability in nonlinear dispersive PDEs set on the line, I
Soliton stability in nonlinear dispersive PDEs set on the line, II
Soliton stability in nonlinear dispersive PDEs set on the line, III
Soliton stability in nonlinear dispersive PDEs set on the line, IV
Soliton stability in nonlinear dispersive PDEs set on the line, V
Soliton stability in nonlinear dispersive PDEs set on the line, VI
Soliton stability in nonlinear dispersive PDEs set on the line, VII