Stability of Nonlinear Waves

What it is about

You learn what traveling waves (solutions that propagate with constant shape and speed) are and why their dynamic stability is important. By the end you can sketch the steps of a stability analysis, understand the associated spectral structure, and apply various tools to approximate spectra and infer (in)stability from spectral data.

What you will be able to do

• Explain the significance of traveling waves and dynamic stability
• Formulate the concept of stability and name the main steps of a stability analysis
• Address possible complications in stability analyses
• Understand the structure of the spectrum associated with a wave
• Master mathematical tools for computing/approximating spectra
• Apply techniques to derive (in)stability from spectral information
• Understand the influence of the disturbance space on the spectrum and stability

What the module consists of

• VorlesungConveying the concepts and methods with examples and discussion
• Übung/PraktikumWorking on concrete examples, supervised tasks and presentation of solutions

Teaching method

• Vortrag mit Demonstrationenpresents content and examples, motivates for own analysis
• Diskussionallows clarification and deepened understanding
• Übungsgruppen mit Präsentationendeepening through supervised tasks, self-check and communication of results