250125 VO Nonlinear Schrödinger equations (2013S)
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Erster Termin: Donnerstag, 7. März 2013
Termine: Do, 14.40 - 15.50, Fr 12.00 - 13.30
Seminarraum C 714 (UZA 4)
Termine: Do, 14.40 - 15.50, Fr 12.00 - 13.30
Seminarraum C 714 (UZA 4)
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 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: 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
Cazenave, Th.:``Semilinear Schroedinger equations'', Courant Lecture Notes 10, AMS, Providence Rhode Island 2003.
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.
Sulem, P.L., Sulem, C.: "The Nonlinear Schrödinger Equation, Self-Focusing and Wave Collapse", Applied Math. Sciences 139, Springer N.Y. 1999
Cazenave, Th.:``Semilinear Schroedinger equations'', Courant Lecture Notes 10, AMS, Providence Rhode Island 2003.
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
MAMV, MANV
Last modified: We 19.08.2020 08:05