Hamiltonian structures for general PDEs

Abstract

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and Kupershmidt's deformation of a bi-Hamiltonian system.

12 pages; v2, v3: minor corrections

References in corpus (4)

• KdV6: An Integrable System
• A new integrable generalization of the Korteweg - de Vries equation
• Homological Methods in Equations of Mathematical Physics
• Integrability of Kupershmidt deformations

Cited by in corpus (8)

• Geometry of jet spaces and integrable systems
• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case
• Integrability of Kupershmidt deformations
• Computing with Hamiltonian operators
• WDVV equations and invariant bi-Hamiltonian formalism
• Jacobi Structures of Evolutionary Partial Differential Equations
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more