Short course: Wave equations, solitons, and stability

29.07. bis 09.08.2024, 14:00 - 16:00  –  Raum 0.14

Lars Andersson

Non-trivial steady states for wave equations and other field equations are often called solitons.
Here I will focus on so-called non-topological solitons. There are many examples of field equations admitting soliton solutions, including non-linear Klein-Gordon, Einstein-Klein-Gordon , Einstein-Yang-Mills, Yang-Mills-Higgs. In this course I will give an introduction to results on local and global existence for non-linear wave equations, discuss examples of steady states, and describe some known facts and open problems concerning the stability properties of solitons.

More information see here.

Some literature:
J. Shatah, M. Struwe, Geometric wave equations, AMS 1998
S. Alinhac, Hyperbolic Partial Differential Equations, Springer 2009
T. D. Lee, Y. Pang, Nontopological solitons (Phys. Rep. 1992)

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