A bi-Hamiltonian approach to the sine-Gordon and Liouville hierarchies

Abstract

In this paper we study the sine-Gordon and the Liouville hierarchies in laboratory coordinates from a bi-Hamiltonian point of view. Besides the well-known local structure these hierarchies possess a second compatible non-local Poisson structure.

17 pages. v2: Additional references

References in corpus (1)

• On the local systems Hamiltonian in the weakly nonlocal Poisson brackets

Cited by in corpus (3)

• Three computational approaches to weakly nonlocal Poisson brackets
• Weakly nonlocal Poisson brackets: tools, examples, computations
• Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics