On the Lagrangian structure of integrable hierarchies

2015/10/13 by Yuri B. Suris, Mats Vermeeren · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.SG #nlin.SI

paper · pdf · doi:10.1007/978-3-662-50447-5_11

published as In: Advances in Discrete Differential Geometry, Ed. A.I. Bobenko, Springer, 2016, p. 347-378 · 29 pages

arxiv created 2015/10/13 · arxiv updated 2019/11/11

Abstract

We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler Lagrange equations in their full generality for hierarchies of two-dimensional systems, and construct a pluri-Lagrangian formulation of the potential Korteweg-de Vries hierarchy.

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