250055 VO Nonlinear Schrödinger Equations (2016S)
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Language: English
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Tues. 13.00 - 14.20 h
Thur. 12.00 - 13.20 h,
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oral exam
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Reading list
Mauser, N.J. and Stimming, H.P. "Nonlinear Schrödinger equations", lecture notes, 2016Sulem, 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.
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.
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MAMV
Last modified: Tu 03.08.2021 00:23
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.Inhalt:
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 resultsMethodenFunctional Analysis, Semigroup theory, Sobolev embeddings, Strichartz estimates, linear PDE theory, Numerical schemes: Finite difference schemes, Spectral methods, Time splitting etc.