The bi-Hamiltonian cohomology of a scalar Poisson pencil

Abstract

We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $B{H}_d^p(\hat{F},d_1,d_2)$ is isomorphic to $\mathbb{R}$ for $(p,d)=(0,0)$, to $C^{\infty }(\mathbb{R})$ for $(p,d)=(1,1)$, $(2,1)$, $(2,3)$, $(3,3)$, and vanishes otherwise.

References in corpus (2)

• Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs

Cited by in corpus (4)

• Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
• Central invariants revisited
• Miura-reciprocal transformations and localizable Poisson pencils
• Normal forms of dispersive scalar Poisson brackets with two independent variables