Continuum limits of integrable lattice systems and their variational structure

Mats Vermeeren, TU Berlin. Part of the integrable systems seminars.

Integrability of lattice systems can be understood as multidimensional consistency. Furthermore, many integrable lattice systems have a variational structure. The notion of a "pluri-Lagrangian" or "Lagrangian multiform" structure combines these two properties. An analogous concept exists in the continuous world for integrable hierarchies of variational differential equations.

We present a procedure to perform the continuum limit of a lattice equation that preserves the pluri-Lagrangian structure. In particular, we recover some well-known hierarchies of PDEs as continuum limits of lattice equations from the ABS list. For some of those hierarchies no pluri-Lagrangian structure was previously known.

Mats Vermeeren, TU Berlin