250073 VO Nonlinear Schrödinger and Wave equations (2020W)
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Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
This course on "Schrödinger and wave equations" for master and PhD students (in MINT - mathematics and physics) is planned as "hybrid" = "half presence teaching in the classroom" plus "half distance teaching with zoom + whiteboard".
Depending on the situation with corona and on the number of students we might also switch to classroom teaching only or distance teaching only.The classroom lectures will be available on moodle as video, too.
Tuesday
06.10.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
07.10.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
13.10.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
14.10.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
20.10.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
21.10.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
27.10.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
28.10.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
03.11.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
04.11.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
10.11.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
11.11.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
17.11.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
18.11.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
24.11.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
25.11.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
01.12.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
02.12.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
09.12.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
15.12.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
16.12.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
12.01.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
13.01.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
19.01.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
20.01.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
26.01.
13:15 - 14:45
Hörsaal 3 Oskar-Morgenstern-Platz 1 Erdgeschoß
Wednesday
27.01.
11:30 - 13:00
Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Oral exam (presence on the blackboard or distance) where the presentation of exercises enters the grade.
Minimum requirements and assessment criteria
The presentation is self-contained based on material
distributed to the students.
Basic knowledge of functional analysis, PDEs and numerical mathematics is helpful.
distributed to the students.
Basic knowledge of functional analysis, PDEs and numerical mathematics is helpful.
Examination topics
The exam is an opportunity to prove the understanding of basic
concepts, own lecture notes etc can be used during the exam.
concepts, own lecture notes etc can be used during the exam.
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.) Tao, Terence:
"Local And Global Analysis of Nonlinear Dispersive And Wave Equations (Cbms Regional Conference Series in Mathematics)", 373 p., American Mathematical Society, 2006.) Ginibre, J.: ``An Introduction to Nonlinear Schroedinger equations'', Hokkaido Univ. Technical Report, Series in Math. 43 (1996), pp. 80-128.
"Local And Global Analysis of Nonlinear Dispersive And Wave Equations (Cbms Regional Conference Series in Mathematics)", 373 p., American Mathematical Society, 2006.) 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: Tu 02.08.2022 00:21
In this lecture we deal with all 3 aspects of "Applied Mathematics”, i.e. = “Modeling + Analysis + Numerics", based on lecture notes that are handed out to students.
1) Modeling: motivation / derivation of NLS :
a) quantum physics, where “one particle” NLS occur as approximate models for the linear N-body Schrödinger equation.
Quantum HydroDynamics.
b) nonlinear optics, where the paraxial approximation of the Helmholtz
(wave) equation yields 2+1 dimensional cubic NLS
2) Analysis:
Existence and Uniqueness (“Local/Global WellPosedness) of NLS and NLW
with local and non-local nonlinearities, scattering, finite(-time) Blow-up; asymptotic results e.g. for the (semi-)classical limit of NLS.
3) Numerics:
Spectral methods, finite difference and relaxation schemes, Absorbing Boundary Conditions, Optimal Control theory...
Methods:
functional analysis, semigroup theory, Sobolev embeddings, Strichartz
estimates, energy estimates, linear PDE theory, … Numerical schemes:
Finite Difference schemes, spectral methods, time splitting, Absorbing
Boundary Layers ("optical potential")
Optimal Control theory