A unified approach to computation of integrable structures

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.

19 pages, based on a talk on the SPT 2011 conference, http://www.sptspt.it/spt2011/ ; v2, v3: minor corrections

References in corpus (3)

• Geometry of jet spaces and integrable systems
• On integrability of the Camassa-Holm equation and its invariants. A geometrical approach
• Variational Poisson-Nijenhuis structures for partial differential equations

Cited by in corpus (7)

• The four-dimensional Martinez Alonso - Shabat equation: differential coverings and recursion operators
• Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations
• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
• Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
• Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras
• Integrable partial differential equations and Lie--Rinehart algebras
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more