Bihamiltonian cohomology of KdV brackets

Abstract

Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups.

16 pages. v2: corrected typos, in particular formulas (28), (78)

References in corpus (2)

• Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case
• On bi-Hamiltonian deformations of exact pencils of hydrodynamic type

Cited by in corpus (7)

• Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
• Central invariants revisited
• Dispersionless (3+1)-dimensional integrable hierarchies
• The bi-Hamiltonian cohomology of a scalar Poisson pencil
• A Darboux-Getzler theorem for scalar difference Hamiltonian operators
• Normal forms of dispersive scalar Poisson brackets with two independent variables
• Miura-reciprocal transformations and localizable Poisson pencils