250050 VO Selected topics in partial differential equations (2009W)

Nichtlineare Schrödinger-Gleichungen

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Erstmals am Donnerstag, 8. Oktober 2009, Do, Fr, 12.30 - 14.00,
C 714 (UZA 4)

Details

Language: German

Lecturers

Classes

Currently no class schedule is known.

Information

Aims, contents and method of the course

* Analysis: Existence and Uniqueness of NLS with local and non-local
nonlinearity, Scattering, Blow-up, Asymptotic results for the
semi-classical limit.
* Modeling: Motivation / Derivation of NLS models in Quantum dynamics
incl. Time Dependent Density Functional Theory and Bose Einstein
Condensates, NLS models in Nonlinear Optics,
* Numerics: methods: Time Splitting Spectral methods and Relaxation
schemes, Validation of Simulation results

Assessment and permitted materials

mündliche Prüfung

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
supervised by the team of the Doktoratskolleg "Differential Equations".

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

Sulem, P.L., Sulem, C.: "The Nonlinear Schrödinger Equation, Self-Focusing and Wave Collapse", Applied Math. Sciences 139, Springer N.Y. 1999

Cazenave, Th.:``Introduction to Nonlinear Schroedinger equations'', Textos de Metodos Matematicos 26, Rio de Janeiro, Instituto de Matematica - UFRJ, 1996.

Bourgain, J.: ``The nonlinear Schrödinger equation'', Colloqium Publications Vol. 46, AMS, Providence R.I. 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

MANV

Last modified: Tu 03.08.2021 00:23