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. Program summaryProgram Title:Jacobi (Maple), CDE module cde_weaklynl.red (Reduce, official distribution), nlPVA (Mathematica)CPC Library link to program files:https://doi.org/10.17632/synmrvr74g.1Developer's repository link:https://gdeq.org/Weakly_nonlocal_Poisson_bracketsLicensing provisions: BSD 2-clauseProgramming language: Maple, Reduce (Rlisp), MathematicaSupplementary material: Example program files in the three languages (Maple, Reduce, Mathematica)Nature of problem: Calculating the Jacobi identity for weakly nonlocal Poisson bracketsSolution method: Bringing the Jacobi identity to a canonical formAdditional comments including restrictions and unusual features: Use a 2020 Maple or Mathematica version, or a 2021 Reduce snapshot