Nonlinear Dynamics and Pattern Formation Winter 15/16

Universität Leipzig
Institut für Theoretische Physik
Prof. Dr. Ulrich Behn

Theoretical Physics in the Master Study Course (12-PHY-MWPTKM2)
Winter Term 2015/16

Nonlinear Dynamics and Pattern Formation

The lecture course is held at the Small Lecture Room of the ITP (Brüderstr. 16, R 114).

Class Times

Monday 13:30-15 (lecture),
Wednesday 11-12:30 (exercise class),
Thursday 9:15-11:45 (lecture)

The oral examination is scheduled to Friday, 19 February 2016: Schedule

The lecture course is intended for students of physics and related disciplines , especially in the first or third semester of their Master Study Course. It will first provide an introduction into the basics of the theory of nonlinear dynamical systems with few degrees of freedom. Then methods to describe systems with (infinitely) many degrees of freedom will be presented. For spatially distributed systems the formation of coherent structures and the pattern formation in driven dissipative systems are discussed. Finally, on an introductory level, we treat systems with temporal delay. Topics include:

Dynamical systems with few degrees of freedom
- Local and global characteristics of flows, classification of singular points, periodic solutions
- Bifurcations, normal forms, central manifolds (enslaving)
- Structural stability, the seven elementary catastrophies
- Chaos in hamiltonian and dissipative systems
Spatially extended systems
- Coherent structures: nonlinear waves, solitons
- Competition of nonlinearity and dispersion or dissipation
- Travelling waves in Burgers, Korteweg de Vries und sin-Gordon equations
- General solution of the Burgers equation, Hopf-Cole transformation, shock waves
- Multi-soliton solution of the KdV equation, inverse scattering method
- Pattern formation in driven systems
- Multiscale analysis, amplitude equation for the Rayleigh-Benard instability
- Phenomenological amplitude equations, Eckhaus and Benjamin-Feir instabilities
- Reaktion-diffusion systems, Turing instability
- Stochastically driven systems, Kardar-Parisi-Zhang equation
Systems with temporal delay

10 credit points are given if an oral exam of about 30 min is passed.

Recommended literatur pdf

Links of interest