Universität Wien

250072 VO Soliton stability in nonlinear dispersive PDEs set on the line (2021S)

2.00 ECTS (1.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes

Location: Erwin Schrödinger Institut für Mathematik und Physik,
Boltzmanngasse 9, 1090 Vienna - virtual via zoom
First lecture: Tuesday 13. April 2021 13:30-15:00
Last lecture: Tuesday 25. May 2021 13:30-15:00

Information

Aims, contents and method of the course

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

Assessment and permitted materials

take-home exam

Minimum requirements and assessment criteria

participation during seminars and take-home exam

Examination topics

exclusively the material discussed in the lectures

Reading list

Association in the course directory

MANV

Last modified: Tu 15.06.2021 15:49