Weakly nonlocal Poisson brackets: tools, examples, computations
Matteo Casati, Paolo Lorenzoni, Daniele Valeri, Raffaele Vitolo
TL;DR
This paper presents an algorithm for computing the Schouten bracket of weakly nonlocal Hamiltonian operators, implemented across three computer algebra systems, facilitating analysis of integrable PDEs.
Contribution
It introduces a novel algorithm for Schouten bracket computation of weakly nonlocal Hamiltonian operators and demonstrates its implementation in Maple, Reduce, and Mathematica.
Findings
Algorithm successfully computes Schouten brackets for weakly nonlocal operators.
Implementation across multiple CAS enhances accessibility and usability.
Applicable to a wide range of (1+1)-integrable PDEs.
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
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