Mathematics 743: Advanced Topics in Differential Equations
(Fall, 2009)

Course Information

Course Objectives: The course covers the basic tools in analysis and numerical approximations of solutions of the nonlinear Schrodinger equation with a particular emphasis on localized modes in periodic potentials. Applications include Bose-Einstein condensation, photonic optics, and superconductivity theory. Both classical techniques (such as Kato-Picard iterations, Floquet analysis, Mountain Pass Theorem, Sylvester Inertial law, and Lyapunov stability) and modern methods (such as symmetry reductions, dynamical system methods, Pontryagin invariant subspaces, numerical iterative algorithms) are reviewed on the case-by-case examples.

Topics: Well-posedness, Hamiltonian structure, justification analysis, existence of stationary and traveling solutions, and stability analysis in the context of the nonlinear Schrodinger equation with a periodic potential and its generalizations.

Instructor: Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail:

Lectures: Monday, Thursday (12:00-13:30), HH-410
Office hours: Monday, Thursday (14:30-15:30)

Coursepack "Localization in periodic potentials" by D. Pelinovsky (McMaster University bookshop, 2009)

Assignments: Five home assignments will be distributed during the classes with specific deadlines.

Presentations: The course is completed by student presentations.

Marking scheme:
Presentation - 50%
Assignments - 50%