Tri-Hamiltonian Structure of the Ablowitz-Ladik Hierarchy
Mathematical Physics
2022-03-14 v1 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We construct a local tri-Hamiltonian structure of the Ablowitz-Ladik hierarchy, and compute the central invariants of the associated bihamiltonian structures. We show that the central invariants of one of the bihamiltonian structures are equal to 1/24, and the dispersionless limit of this bihamiltonian structure coincides with the one that is defined on the jet space of the Frobenius manifold associated with the Gromov-Witten invariants of local CP1. This result provides support for the validity of Brini's conjecture on the relation of these Gromov-Witten invariants with the Ablowitz-Ladik hierarchy.
Keywords
Cite
@article{arxiv.2108.03447,
title = {Tri-Hamiltonian Structure of the Ablowitz-Ladik Hierarchy},
author = {Shuangxing Li and Si-Qi Liu and Haonan Qu and Youjin Zhang},
journal= {arXiv preprint arXiv:2108.03447},
year = {2022}
}