### Ringvorlesung Wave Phenomena (Summer Semester 2016)

- Lecturer: Prof. Dr. Willy Dörfler, Prof. Dr. Roland Schnaubelt
- Classes: Lecture (0162200)
- Weekly hours: 2
- Audience: Mathematics, CRC 1173 (from 8. semester)

In the RTG lecture series four members of CRC 1173 will talk about topics whithin the analysis and numerics of wave phenomena. The lectures are directed to Ph.D. students (in particular of the integrated research training group of CRC 1173) and to advanced master students with a solid backbground in partial differential equations. The series is organized by Willy Dörfler and Roland Schnaubelt.

Schedule | |||
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Lecture: | Monday 14:00-15:30 | SR 1.067 | Begin: 18.4.2016 |

Lecturers | ||
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Lecturer | Prof. Dr. Dirk Hundertmark | |

Office hours: | ||

Room 2.028 Kollegiengebäude Mathematik (20.30) | ||

Email: dirk.hundertmark@kit.edu | ||

Lecturer | Prof. Dr. Roland Schnaubelt | |

Office hours: Tuesday at 12:00 - 13:00, and by appointment. | ||

Room 2-047 (Englerstr. 2) Kollegiengebäude Mathematik (20.30) | ||

Email: schnaubelt@kit.edu | ||

Lecturer | JProf. Dr. Katharina Schratz | |

Office hours: By Appointment | ||

Room Kollegiengebäude Mathematik (20.30) | ||

Email: |

## 1) Roland Schnaubelt: Symmetric hyperbolic systems

Symmetric hyperbolic systems are a general class of evoluttionary partial differential equations of first order which comprise the Maxwell system or the Euler equations. We focus on the wellposedness of linear problems with constant coefficients on the full and the half space (the latter with boundary conditions). The variable-coeffcient case and quasilinear problems will be sketched if there is enough time. We use the Fourier transform and basic semigroup theory (Lumer-Phillips). The lectures take place on

- 18 April - 9 May

and are based on the first sections of

- S. Benzoni-Gavage and D. Serre: Multidimensional Hyperbolic Partial Differential Equations. Clarendon Press, 2007.

## 2) Dirk Hundertmark: Discrete dispersion management solitons

The lectures will be given on 23 and 30 May and on 16 and 20 June. The lecture on 16 June also takes place

in SR 1.067 from 14:00 to 15:30.

## 3) Christian Koos: Integrated photonics and data transmission

The lectures will be given on 27 June and 4 July.

Christian Koos is professor at the Institute of Photonics and Quantum Electronics and head of the Institute of Microstructure Technology.

## 4) Katharina Schratz: Aspects of numerical time integration.

In this lecture we illustrate some ideas in the convergence analysis of splitting as well as exponential integrator methods for semilinear evolution equations. As a model problem we will thereby consider the cubic Schrödinger equation. If time allows, we also show some techniques concerning the time integration of certain dispersive equations involving a derivative in the nonlinearity, e.g., the Zakharov system (a scalar model for Langmuir oscillations in a plasma). Furthermore, we want to give the students the opportunity to do some programming on their own (during the lecture) for some easier test problems using Fourier pseudo spectral methods for the space discretization. References:

- E. Faou, Geometric Numerical Integration and Schrödinger Equations. European Math. Soc., 2012.

- C. Lubich, On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Math. Comp. 77:2141--2153 (2008).

The lectures will be given on 11 and 18 July.