Seminar sessions Friday 10–12, room 2.040 (Endenicher Allee 60).
A preliminary meeting will be on Friday, 25.09.15 at 10.15am in room 2.040.
Waves are an essential and ubiquitous part of our world and they intrigue many people: music-lovers listening to their favourite songs, children throwing stones across the pond, or mathematicians and physicists studying them. Corresponding models for wave propagation contain many interesting dynamic phenomena.
In the seminar, we will consider some of these phenomena and methods for certain wave models and equations. Topics will be selected from
- Geometrical optics, e. g. propagation of waves in terms of rays; reflection, refraction and diffraction;
- Solitons, i. e. localized waves that do not change form and interact with other waves "elastically";
- Scattering and the Inverse Scattering Method;
- Defects, e. g. interfaces and vortices;
- Smoothing properties.
Basic knowledge of PDEs is essential, complex analysis is useful.
The seminar sessions will be on Fridays 10–12, room is tbc.
Topics are distributed in the preliminary meeting on 25.09.15. Interested students who cannot attend this meeting are asked to contact us by email.
- M. J. Ablowitz. Solitons, nonlinear evolution equations and inverse scattering. Cambridge University Press, 1991.
- P. Constantin and J. C. Saut. Local smoothing properties of dispersive equations. J. Amer. Soc. Math. 1, 413–439, 1988.
- R. Jerrard. Defects in semilinear wave equations and timelike minimal surfaces in Minkowski space. Anal. PDE 4, 285–340, 2011.
- J. B. Keller. Geometrical theory of diffraction. J. Opt. Soc. Amer. 52, 116–130, 1962.
- P. D. Lax. Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21, 467–490, 1968.