250312 VO Nonlinear Schrödinger Equations (2007S)
Nonlinear Schrödinger Equations
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Erstmals am Mittwoch, 7. März 2007; Mi 12.30 - 13.15 Uhr, Do 12.30 - 14.00 Uhr, WPI C 714 (UZA 4)
Details
Language: German
Lecturers
Classes
Currently no class schedule is known.
Information
Aims, contents and method of the course
Assessment and permitted materials
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 Wissenschaftskolleg "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.
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. 1999Cazenave, 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. 1999Ginibre, J.: ``An Introduction to Nonlinear Schroedinger equations'', Hokkaido Univ. Technical Report, Series in Math. 43 (1996), pp. 80-128.
Association in the course directory
Last modified: Tu 03.08.2021 00:23
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