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This article is cited in 4 scientific papers (total in 4 papers)
A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations
Mats Vermeeren Institut für Mathematik, MA 7-1, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
Abstract:
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.
Keywords:
continuum limits, pluri-Lagrangian systems, Lagrangian multiforms, multidimensional consistency.
Received: November 20, 2018; in final form May 16, 2019; Published online June 3, 2019
Citation:
Mats Vermeeren, “A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations”, SIGMA, 15 (2019), 044, 35 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1480 https://www.mathnet.ru/eng/sigma/v15/p44
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Abstract page: | 125 | Full-text PDF : | 25 | References: | 21 |
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