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Course Description

Wave propagation subject to nonlinear effects occurs in physical systems as diverse as the atmosphere, ocean surface waves, lasers, magnets, and quantum particles, and such systems are modelled by PDE known collectively as "nonlinear wave equations". Qualitatively, behaviour in these systems is often characterized by a competition between dispersive (spreading-out, wave-like) and nonlinear (concentrating, enhancing) effects. Mathematically, the study of these PDE has become one of the dominant research areas in analysis, combining as it does functional and harmonic analysis, and concepts from mathematical physics, Hamiltonian systems, and ODE theory. This course develops the mathematical tools used to address the most important questions concerning nonlinear wave equations as models of physical phenomena: Can solutions be uniquely defined locally in time? Do solutions exist for all time, or do they "blow up" in finite time? If a solution exists for all time, how does it look like after a long time? Does it become trivial? Does it settle down to some interesting configuration?


Here is the tentative outline. It can be adjusted according to audience background and interests.


Files of some references will be available in a public owncloud folder, whose link will be given.


Basic properties of Sobolev spaces and Fourier transform will be needed throughout the course, and will be reviewed in the beginning of the course.


The evaluation is based on homework assignments and class participation.

Instructor and lectures

Instructor: Dr. Tai-Peng Tsai, Math building room 109, phone 604-822-2591, ttsai at

Lectures: MWF, 13:00 - 13:50, Math Annex MATX 1102

Office hours: TBA, and by appointment (Tsai's schedule).