### A new variational principle for integrable systems

- Series
- Analysis Seminar
- Time
- Tuesday, April 7, 2015 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Sarah Lobb – University of Sidney

The conventional point of view is that the Lagrangian is a scalar
object, which through the Euler-Lagrange equations provides us with one
single equation. However, there is a key integrability property of certain
discrete systems called multidimensional consistency, which implies that we
are dealing with infinite hierarchies of compatible equations. Wanting this
property to be reflected in the Lagrangian formulation, we arrive naturally
at the construction of Lagrangian multiforms, i.e., Lagrangians which are
the components of a form and satisfy a closure relation. Then we can
propose a new variational principle for discrete integrable systems which
brings in the geometry of the space of independent variables, and from this
principle derive any equation in the hierarchy.