On integrability of some bi-Hamiltonian two field systems of PDE

TL;DR

This paper investigates the integrability of certain bi-Hamiltonian PDE systems using compatible Poisson structures, introducing new two-field integrable models linked to the cohomology of moduli spaces of curves.

Contribution

It presents new integrable two-field PDE systems derived from compatible Poisson structures related to moduli space cohomology.

Findings

Identification of new integrable two-field PDE systems

Application of compatible Poisson structures in system construction

Connection to cohomology of moduli spaces of curves

Abstract

We continue the study of integrability of bi-Hamiltonian systems with a compatible pair of local Poisson structures (H_0,H_1), where H_0 is a strongly skew-adjoint operator. This is applied to the construction of some new two field integrable systems of PDE by taking the pair (H_0,H_1) in the family of compatible Poisson structures that arose in the study of cohomology of moduli spaces of curves.