Properties of Moyal-Lax Representation

Abstract

The Moyal-Lax representation and the Moyal momentum algebra are introduced and systematically investigated. It is shown that the Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. We show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The Moyal-Lax description leads in a natural manner to the dispersionless limit and provides the second Hamiltonian structure of dispersionless integrable models, which has been an open question for sometime.

11 pages, references added, version to be published in Phys. Letters B

Cited by in corpus (7)

• Classical R-matrix theory for bi-Hamiltonian field systems
• From dispersionless to soliton systems via Weyl-Moyal like deformations
• Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Integrable discrete systems on R and related dispersionless systems
• Lucas polynomials and a standard Lax representation for the polytropic gas dynamics
• Conformal Covariantization of Moyal-Lax Operators