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Variational principle for discrete 2d integrable systems

Lobb, S (University of Sydney)
Wednesday 10 July 2013, 10:00-10:30

Seminar Room 1, Newton Institute


For multidimensionally consistent systems we can consider the Lagrangian as a form, closed on the multidimensional equations of motion. For 2-d systems this allows us to define an action on a surface embedded in higher dimensions. It is then natural to propose that the system should be derived from a variational principle which includes not only variations with respect to the dependent variables, but also variations of the surface in the space of independent variables. I will describe how this puts constraints on the Lagrangian, and how this leads to equations on a single quad in the lattice.


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