Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems
Dr Raphael Boll
Technische Universität Berlin, Germany
We establish the pluri-Lagrangian structure for families of Bäcklund transformations of relativistic Toda-type systems. This is a generalization of the results of our recent paper on non-relativistic Toda-type systems. However, we present an alternative approach to this theory using the pluri-Lagrangian structure of related two-dimensional variational equations which we discussed in another recent paper. Some but not all of them have their origin in the Lagrangian structure of quadequations. Also in this situation, we have to deal with the multi-valuedness of the case of periodic boundary conditions and again we describe the branching behaviour by usage of so-called superposition formulas. The proofs of the closure relation are a more or less direct consequence of the similar results of the related two-dimensional variational equations.