Special Colloquium
Irina Nenciu
Courant Institute
On the Toda and Ablowitz-Ladik equations: comparing two discrete completely integrable systems
Abstract: Completely integrable systems are remarkable evolution
equations, the best known of which is probably the Korteweg-deVries
equation. Their many ``symmetries'', or conserved quantities, often allow
for a detailed and in-depth description of their solutions.
We will present a number of new results concerning the
Ablowitz-Ladik equation (AL). This is a classical, completely integrable
discretization of the nonlinear Schroedinger equation. We will contrast
its properties with those of one of the most celebrated discrete
integrable system, the Toda lattice, while also illustrating the varied
nature of the tools and ideas involved in the theory of completely
integrable systems: geometric, algebraic, and functional analytic, among
others.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Friday January 25, 2008 at 3:00 PM in SEO 636