# Continuum limits of integrable lattice systems and their variational structure

**Date**: Friday 3 November 2017, 14:30 – 15:30**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Applied Mathematics seminars, Integrable systems seminars, Seminar series**Cost**: Free

#### 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*