Seminar (Differential equations)
|SE 2 std.||Mi 13:15-14:45||2A180||3.10|
Recently it was shown that these ideas, originally developed for finite-dimensional Hamilton's equations, also apply to certain partial differential equations which can be viewed as infinite-dimensional Hamiltonian systems. This has played an important role in the development of soliton theory and the prototypical integrable wave equation is the famous Korteweg-de Vries equation.
We will try to shed some light on this circle of ideas following the book of Kappeler and Pöschl. A solid background in analysis and differential equations will be assumed, but no previous knowledge about Hamiltonian systems will be neccesary.
|07.11||Background from differential geometry||Jonathan Eckhardt||[MR]|
|14.11||Hamiltonian Formalism||Katharina Kienecker||[KP]|
|21.11||Liouville Integrable Systems||Manfred Buchacher||[KP]|
|28.11||Birkhoff Integrable Systems||Alexander Beigl||[KP,M]|
|05.12||KAM Theory||Markus Holzleitner||[KP,W]|
|09.01||Background and Results||Aleksey Kostenko||[KP]|
- T. Kappeler and J. Pöschl, KdV & KAM, Springer 2003.
- J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Springer 1999.
- J. Moser, Lectures on Hamiltonian systems, Memoires of the Amer. Math. Soc. 81 (1968), 1-60.
- C. E. Wayne, An Introduction to KAM Theory, Notes.