Weakly nonlocal Poisson brackets: Tools, examples, computations

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. Program summary Program Title: Jacobi(Maple), CDEmodulecde_weaklynl.red(Reduce, official distribution), nlPVA(Mathematica) CPC Library link to program files: https://doi.org/10.17632/synmrvr74g.1 Developer's repository link: https://gdeq.org/Weakly_nonlocal_Poisson_brackets Licensing provisions: BSD 2-clause Programming language: Maple, Reduce (Rlisp), Mathematica Supplementary material: Example program files in the three languages (Maple, Reduce, Mathematica) Nature of problem: Calculating the Jacobi identity for weakly nonlocal Poisson brackets Solution method: Bringing the Jacobi identity to a canonical form Additional comments including restrictions and unusual features: Use a 2020 Maple or Mathematica version, or a 2021 Reduce snapshot (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

We have implemented an algorithm for computing the Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems. This algorithm can handle almost all examples coming from the theory of (1+1)-integrable evolutionary PDEs.