Extension of Moyal-deformed hierarchies of soliton equations

Abstract

Moyal-deformed hierarchies of soliton equations can be extended to larger hierarchies by including additional evolution equations with respect to the deformation parameters. A general framework is presented in which the extension is universally determined and which applies to several deformed hierarchies, including the noncommutative KP, modified KP, and Toda lattice hierarchy. We prove a Birkhoff factorization relation for the extended ncKP and ncmKP hierarchies. Also reductions of the latter hierarchies are briefly discussed. Furthermore, some results concerning the extended ncKP hierarchy are recalled from previous work.

arXiv comment15 pages, proceedings XI-th International Conference Symmetry Methods in Physics (Prague, June 2004)

References in corpus (5)

• Exact Noncommutative KP and KdV Multi-solitons
• Nonabelian KP hierarchy with Moyal algebraic coefficients
• Towards Noncommutative Integrable Equations
• Deformations of dispersionless KdV hierarchies
• WDVV equation and Triple-product Relation

Cited by in corpus (5)

• An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions
• A new approach to deformation equations of noncommutative KP hierarchies
• Noncommutative Integrable Systems and Quasideterminants
• Soliton Scattering in Noncommutative Spaces
• Bilinear identities for an extended B-type Kadomtsev-Petviashvili hierarchy