INTEGRABLE SYSTEMS - METHODS OF MATHEMATICAL PHYSICS IN INTERACTION
PROF. Cornelia SCHIEBOLD
Mid Sweden University, Sundsvall, Sweden
Integrable systems in infinite dimension refer to an area in
mathematical physics which is devoted to the study of a certain group of
partial differential equations, many of them soliton equations like the
classic Korteweg-de Vries equation and the nonlinear Schrodinger
equation. One of the striking features is the existence of solutions
with particle character, called solitons, remarkable in view of
nonlinearity of the governing equations. Methodologically, integrable
systems are a meeting point (melting pan) for methods from very diverse
parts of mathematics. The main idea of this mini course is to highlight
interactions of some of the main approaches to integrable systems, the
inverse scattering method and an operator theoretic approach in the
first place, and symmetry methods like Backlund transformations,
recursion operators and hierarchies to a minor extent.
Throughout we will emphasise the recent topic ofnon-commutative
integrable systems, like vector- and matrix soliton equations, where
many fundamental questions are still open. Notably, the construction of
solutions is not interesting only under the mathematical viewpoint, but
also under the physical one. Indeed, very important applications of
soliton equations are in nonlinear optics, for instance.
The lectures are going to be reasonably self-contained. Some familiarity
with PDE's and functional analysis is certainly helpful, but not
required. An overview on the basic notions used during the course are
provided when needed.
The course is organised in six lectures (a two hours lecture each week
as indicated below).
Needed material as well as references are provided by the Lecturer.
AULA 1B1 PAL RM002
* Lectures 1-2 March 7 time 12-14
* Lectures 3-4 March 14 time 12-14
* Lectures 5-6 March 21 time 12-14