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A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2019_15_a43,
     author = {Mats Vermeeren},
     title = {A {Variational} {Perspective} on {Continuum} {Limits} of {ABS} and {Lattice} {GD} {Equations}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a43/}
}
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Mats Vermeeren. A Variational Perspective on Continuum Limits of ABS and Lattice GD Equations. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a43/

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