Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

Abstract

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.

43 pages. V2: the accepted version, to appear in Comm. Math. Phys

References in corpus (5)

• The variational Poisson cohomology
• On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs
• Essential variational Poisson cohomology
• Hamiltonian structures for general PDEs
• On bi-Hamiltonian deformations of exact pencils of hydrodynamic type

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• Bihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures
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• Central Invariants of the Constrained KP Hierarchies
• Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
• Bihamiltonian cohomology of KdV brackets
• Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
• Three computational approaches to weakly nonlocal Poisson brackets
• The calculus of multivectors on noncommutative jet spaces
• Towards a bihamiltonian structure for the double ramification hierarchy
• Deformations of non semisimple Poisson pencils of hydrodynamic type
• Central invariants revisited
• The bi-Hamiltonian cohomology of a scalar Poisson pencil
• On integrable conservation laws
• Super tau-covers of bihamiltonian integrable hierarchies
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro symmetries
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations
• Normal forms of dispersive scalar Poisson brackets with two independent variables
• Miura-reciprocal transformations and localizable Poisson pencils
• Tri-Hamiltonian Structure of the Ablowitz-Ladik Hierarchy
• Frobenius Manifolds, Spectral Curves, and Integrable Hierarchies
• Bi-Hamiltonian structures of KdV type