Lagrangian multiforms and integrability of lattice systems
Sarah Lobb (University of Leeds)
Tuesday 2nd March, 2010 15:00-16:00 Mathematics Building, room 204
The conventional point of view is that the Lagrangian is a scalar object (or equivalently a volume form), which through the Euler-Lagrange equations provides us with one single equation (i.e. one per component of the dependent variable). In the case of an integrable system, multidimensional consistency means that several equations can be imposed simultaneously on one and the same dependent variable. We propose that the Lagrangian should reflect this property, that it should be a multiform from which copies of the equation in all possible directions can be derived. This requires a new variational principle for integrable systems which involves the geometry of the space of independent variables.