Universität Wien FIND
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250076 VO Nonlinear Schrödinger and Wave Equations (2017S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: Englisch

Examination dates

Lecturers

Classes

Erster Termin: Di. 07.03.
Termine: Di 12:00-13:00 und Do 11:50-13:50 Uhr
Ort : OMP1, 8. Stock, WPI Seminarraum 08.135


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 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.

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

Examination topics

Reading list

.) Mauser, N.J. and Stimming, H.P. "Nonlinear Schrödinger equations", lecture notes

.) 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: Th 29.06.2017 10:10