On a class of third-order nonlocal Hamiltonian operators
arXiv:1805.00746 · doi:10.1016/j.geomphys.2018.10.018
Abstract
Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by a Monge metric and a skew-symmetric two-form satisfying a number of differential-geometric constraints. Complete classification results in the 2-component and 3-component cases are obtained.
arXiv comment19 pages
References in corpus (8)
- Poisson vertex algebras in the theory of Hamiltonian equations
- Non-local Poisson structures and applications to the theory of integrable systems
- Projective-geometric aspects of homogeneous third-order Hamiltonian operators
- Alternative bi-Hamiltonian structures for WDVV equations of associativity
- Systems of conservation laws with third-order Hamiltonian structures
- Towards the classification of homogeneous third-order Hamiltonian operators
- A counterpart of the WKI soliton hierarchy associated with so(3,R)
- Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets
Cited by in corpus (6)
- Computing with Hamiltonian operators
- Three computational approaches to weakly nonlocal Poisson brackets
- Bi-Hamiltonian structure of the Oriented Associativity Equation
- WDVV equations and invariant bi-Hamiltonian formalism
- Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics
- WDVV equations: Hamiltonian operators and symbolic computations