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Nonlinear Schrödinger Equations: Dynamical Aspects (Summer Semester 2010)

Schedule
Lecture: Monday 14:00-15:30 1C-03 (Allianzgebäude 05.20) Begin: 12.4.2010
Lecturers
Lecturer Prof. Dr. Roland Schnaubelt
Office hours: Wednesday, 11:30 - 13:00, and by appointment
Room 2-047 (Englerstr. 2) Kollegiengebäude Mathematik (20.30)
Email: schnaubelt@kit.edu

The nonlinear Schrödinger equation (NLS) arises in various areas in physics. As an important example we mention nonlinear optics where the NLS approximatively describes evelope functions of wave packets. The NLS has attracted a lot of interest in mathematics in recent years and it has been treated using a great variety of methods. In this lecture we give an introduction to the analysis of the (non-stationary) NLS. We want to treat the following topics:

  • Heuristics and derivation
  • Linear theory and Strichartz estimates
  • Local wellposedness
  • Global wellposedness
  • Stability of standing waves

Prerequistes are (the contents of) the lectures functional analysis and spectral theory.

Further informations concerning this lecture you find in the Studierendenportal of the KIT at the URL https://studium.kit.edu/sites/vab/66161/Start/homepage.aspx

References

  • T. Cazenave: Semilinear Schrödinger Equations. AMS 2003.
  • J.V. Moloney and A.C Newell: Nonlinear Optics. Westview Press 2004.
  • J.A. Pava: Nonlinear Dispersive Equations. AMS 2009.
  • C. and P.-L. Sulem: The Nonlinear Schrödinger Equation. Springer 1999.
  • T. Tao: Nonlinear Dispersive Equations. AMS 2006.