Variational Poisson-Nijenhuis structures for partial differential equations

Abstract

We explore variational Poisson-Nijenhuis structures on nonlinear PDEs and establish relations between Schouten and Nijenhuis brackets on the initial equation with the Lie bracket of symmetries on its natural extensions (coverings). This approach allows to construct a framework for the theory of nonlocal structures.

12 pages; v2: the content isn't changed, submission metadata fixed; v3: a minor correction

References in corpus (2)

• Hamiltonian operators and l*-coverings
• A geometric study of the dispersionless Boussinesq type equation

Cited by in corpus (8)

• Geometry of jet spaces and integrable systems
• A unified approach to computation of integrable structures
• On integrability of the Camassa-Holm equation and its invariants. A geometrical approach
• Variational Lie algebroids and homological evolutionary vector fields
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• A family of second Lie algebra structures for symmetries of dispersionless Boussinesq system
• Non-Abelian Lie algebroids over jet spaces
• Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models