Tri-Hamiltonian Structure of the Ablowitz-Ladik Hierarchy

Shuangxing Li; Si-Qi Liu; Haonan Qu; Youjin Zhang

doi:10.1016/j.physd.2022.133180

paper

Tri-Hamiltonian Structure of the Ablowitz-Ladik Hierarchy

arXiv:2108.03447 · doi:10.1016/j.physd.2022.133180

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.