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

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.

30 pages

References in corpus (1)

• Singular degree of a rational matrix pseudodifferential operator

Cited by in corpus (3)

• Projective geometry of homogeneous second order Hamiltonian operators
• MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine $\mathcal{W}$-algebras
• Two-component integrable generalizations of Burgers equations with nondiagonal linearity