On the Lagrangian structure of integrable hierarchies. (English) Zbl 1408.37120
Bobenko, Alexander I. (ed.), Advances in discrete differential geometry. Berlin: Springer. 347-378 (2016).
Summary: 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.
For the entire collection see [Zbl 1354.53005].
For the entire collection see [Zbl 1354.53005].
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 58E30 | Variational principles in infinite-dimensional spaces |
| 70H30 | Other variational principles in mechanics |
| 39A12 | Discrete version of topics in analysis |
Keywords:
pluri-Lagrangian structures; integrable hierarchies; Lagrangian multiform; multi-time Euler Lagrange equation; Korteweg-de Vries hierarchyReferences:
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