Noncommutative Generalized NS and Super Matrix KdV Systems from a Noncommutative Version of (Anti-) Self-Dual Yang-Mills Equations

Abstract

A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrodinger (NS) equations, of the super-Korteweg- de Vries (super-KdV) as well as of the matrix KdV equations. Noncommutative extensions of their linear systems and bicomplexes associated to conserved quantities are discussed.

15 pages

References in corpus (1)

• Anti-self-dual Yang-Mills equations on noncommutative spacetime

Cited by in corpus (11)

• Noncommutative Multi-Solitons in 2+1 Dimensions
• Towards Noncommutative Integrable Systems
• Integrable Noncommutative Sine-Gordon Model
• Exact Noncommutative KP and KdV Multi-solitons
• Some properties of the integrable noncommutative sine-Gordon system
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Towards Noncommutative Integrable Equations
• Interaction of Noncommutative Plane Waves in 2+1 Dimensions
• Quasideterminant solutions of NC Painlevé II equation with the Toda solution at $n=1$ as a seed solution in its Darboux transformation
• Topics in noncommutative integrable theories and holographic brane-world cosmology
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane