Each lecture will be accompanied by a problem set that revisits and expands on a selection of topics from the lecture. These exercises will be discussed in the exercise session on Thursdays, according to the following two-week rhythm:
The context of each exercise, and possibly hints towards its solution, are given.
You have one week to work on solutions and hand them in.
Another week later, written solutions are provided and discussed in the exercise session.
While you are not required to hand in solutions, you are encouraged to do so. Irrespective of this, you should present (at least) one problem and its solution in an exercise session (starting with problem set 2).
Here you find the current draft of the lecture notes. They will be revised and expanded on a running basis. All comments are welcome, in particular also reports on typos.
The aim of this course is to provide an introduction to the rigorous mathematical analysis of solutions to partial differential equations with dispersive or wave features. Classical such examples are the (nonlinear) Schrodinger, wave or KdV equations. These are time evolution problems that arise in many physically relevant contexts, such as quantum mechanics, electrodynamics, fluid motion and relativity theory.
Literature
The course will be accompanied by lecture notes, which will be published on a rolling basis. A core part of the lecture material can be found in
"Introduction to nonlinear dispersive equations" by F. Linares & G. Ponce most accessible, and closest to the lecture (available online)
Futher book recommendations are
"Nonlinear dispersive equations. Local and global analysis" by T. Tao a classic - highly recommended, but challenging (and likely too extensive)
"Geometric wave equations" by J. Shatah & M. Struwe more focus on wave equations
"Semilinear Schrödinger Equations" by T. Cazenave much more about the Schrödinger Equation
"Dispersive Partial Differential Equations - Wellposedness and Applications" by M. B. Erdogan and N. Tzirakis a different perspective, emphasis on periodic domains
Exam
The exam will be oral, 30 minutes duration. Topics include all material from the lecture and the exercises. Active participation in the exercise session is thus highly encouraged.
