250076 VO Nonlinear Schrödinger and Wave Equations (2017S)

Analysis: Existence and Uniqueness of NLS and NLW with local and non-local nonlinearity, scattering, Blow-up, asymptotic results e.g. for the semi-classical limit of NLS.

Modeling: Motivation / Derivation of quantum wave equations

Numerics: methods: Spectral methods, finite difference and relaxation schemes, Absorbing Boundary Conditions, Validation of simulation results

Functional Analysis, Semigroup theory, Sobolev embeddings, Strichartz estimates, linear PDE theory, Numerical schemes: Finite difference schemes, Spectral methods, Time splitting etc.

Introduction to a very active field of PDE research and to some of the modern methods. Both masters thesis and PhD thesis in the field are possible, funded by projects.