Weakly nonlocal Poisson brackets: tools, examples, computations

Abstract

We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematica. This class of Hamiltonian operators encompass almost all the examples coming from the theory of (1+1)-integrable evolutionary PDEs

30 pages. Keywords: Poisson bracket, Hamiltonian operator, Schouten bracket, partial differential equations, integrable systems

References in corpus (1)

• WDVV equations and invariant bi-Hamiltonian formalism

Cited by in corpus (5)

• Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures
• Miura-reciprocal transformations and localizable Poisson pencils
• Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics
• WDVV equations: Hamiltonian operators and symbolic computations
• Bi-Hamiltonian structures of WDVV-type