Computing with Hamiltonian operators
arXiv:1808.03902 · doi:10.1016/j.cpc.2019.05.012
Abstract
Hamiltonian operators are used in the theory of integrable partial differential equations to prove the existence of infinite sequences of commuting symmetries or integrals. In this paper it is illustrated the new Reduce package \cde for computations on Hamiltonian operators. \cde can compute the Hamiltonian properties of skew-adjointness and vanishing Schouten bracket for a differential operator, as well as the compatibility property of two Hamiltonian operators and the Lie derivative of a Hamiltonian operator with respect to a vector field. It can also make computations on (variational) multivectors, or functions on supermanifolds. This can open the way to applications in other fields of Mathematical Physics.
35 pages, published version; software is available on the web page of the author http://poincare.unisalento.it/vitolo
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- Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures
- Bi-Hamiltonian structure of the Oriented Associativity Equation
- Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures
- Weakly nonlocal Poisson brackets: tools, examples, computations
- Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds
- Classification of degenerate non-homogeneous Hamiltonian operators
- WDVV equations and invariant bi-Hamiltonian formalism
- Bi-Hamiltonian structures of WDVV-type