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250114 VO Nonlinear Schrödinger and Wave Equations (2014S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Erster Termin: Di. 04.03.
Termine: Di und Do 12.30 -14.00 Uhr
OMP1, 8. Stock, WPI Seminarraum 08.135

Details

Language: English

Examination dates

Lecturers

Classes

Currently no class schedule is known.

Information

Aims, contents and method of the course

Analysis: Existence and Uniqueness of NLS and NLW with local and non-local nonlinearity, scattering, Blow-up, asymptotic results 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

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

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.

Examination topics

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

Reading list

Mauser, N.J. and Stimming, H.P. "Nonlinear Schrödinger equations", lecture
notes, 2011 Sulem, P.L., Sulem, C.: "The Nonlinear Schrödinger Equation,
Self-Focusing and Wave Collapse", Applied Math. Sciences 139, Springer
N.Y. 1999 Ginibre, J.: ``An Introduction to Nonlinear Schroedinger equations'', Hokkaido Univ. Technical Report, Series in Math. 43 (1996), pp. 80-128.

Association in the course directory

MAMV, MANV

Last modified: We 19.08.2020 08:05