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

Alberto De Sole, Victor G. Kac, Refik Turhan

Published 2014-05-06Version 1

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.