Symmetry Integrability and Geometry-Methods and Applications | |
A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations | |
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
【 预 览 】
Files | Size | Format | View |
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RO202106300000783ZK.pdf | 548KB | download |