6 Feb 2019 Wed 12:00-13:00
8 Feb 2019 Fri 14:30-15:30
Dept Math & Stat (UiT), room A036

Evgeny Ferapontov (Loughborough University, UK)

"Integrability in 1+1 and 2+1 dimensions: an introduction".

Integrable systems in 1+1 dimensions have been investigated by a whole variety of complementary techniques including the symmetry approach, bi-Hamiltonian formalism and the inverse scattering transform. Unfortunately, the classifications techniques from 1+1 dimensions do not generalise to higher dimensions in a straightforward way due to non-locality of higher symmetries. These lectures will review the classical results and introduce an alternative techniques of classification of 2+1 dimensional integrable systems based on the method of hydrodynamic reductions.

The lectures this week will cover the following topics:

L1: Different approaches to integrability in 1+1D. Example of the Korteweg de Vries equation (slides).
L2: Hamiltonian formalism in finite and infinite dimensions (notes from the blackboard talk).