A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations

Symmetry Integrability and Geometry-Methods and Applications

article

Mats Vermeeren¹ 

[1] Institut für Mathematik

关键词: continuum limits;    pluri-Lagrangian systems;    Lagrangian multiforms;    multidimensional consistency;   

DOI  :  10.3842/SIGMA.2019.044

来源: National Academy of Science of Ukraine

【 摘 要 】

A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consistency (in the discrete case) or commutativity of the flows (in the continuous case) with a variational principle. Recently we developed a continuum limit procedure for pluri-Lagrangian systems, which we now apply to most of the ABS list and some members of the lattice Gelfand-Dickey hierarchy. We obtain pluri-Lagrangian structures for many hierarchies of integrable PDEs for which such structures where previously unknown. This includes the Krichever-Novikov hierarchy, the double hierarchy of sine-Gordon and modified KdV equations, and a first example of a continuous multi-component pluri-Lagrangian system.

【 授权许可】

Unknown