Bicomplexes, Integrable Models, and Noncommutative Geometry

Abstract

We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.

arXiv comment6 pages, 1 figure, LaTeX using amssymb.sty and diagrams.sty, to appear in Proceedings of the 1999 Euroconference "Noncommutative geometry and Hopf algebras in Field Theory and Particle Physics"

References in corpus (2)

• A Geometry for Multidimensional Integrable Systems
• Soliton equations and the zero curvature condition in noncommutative geometry

Cited by in corpus (16)

• Towards Noncommutative Integrable Systems
• Noncommutative Burgers Equation
• Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies
• Isospectral Hamiltonians from Moyal products
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• The U(N) chiral model and exact multi-solitons
• Bicomplexes and Backlund transformations
• Bicomplex formulation and Moyal deformation of (2+1)-dimensional Fordy-Kulish systems
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• On non commutative sinh-Gordon Equation
• Abelian Toda field theories on the noncommutative plane
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• Bicomplexes and Conservation Laws in Non-Abelian Toda Models
• Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space