A unified approach to computation of integrable structures

TL;DR

This paper presents a unified, coordinate-based computational approach to integrable structures in partial differential equations, focusing on recursion, Hamiltonian, and symplectic operators, aimed at providing a tutorial for researchers.

Contribution

It introduces a comprehensive, geometrically inspired computational framework for integrable structures, unifying various operators within a coordinate-based methodology.

Findings

Provides a systematic computational method for integrable structures

Unifies recursion, Hamiltonian, and symplectic operators under one framework

Serves as a tutorial for researchers in the field

Abstract

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based approach and aim to provide a tutorial to the computations.