Towards Noncommutative Integrable Systems

Details Towards Noncommutative Integrable Systems Towards Noncommutative Integrable Systems

2002-11-18

arxiv.org/abs/hep-th/0211148v3

Phys.Lett. A316 (2003) 77-83

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 1 figure, LaTeX; v2: typos corrected, comments and references added; v3: comments and references added, version to a

Scientific paper

10.1016/S0375-9601(03)01138-1

We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the bicomplex method and by reductions of the noncommutative (anti-)self-dual Yang-Mills equation. This suggests that the noncommutative Lax equations would be integrable and be derived from reductions of the noncommutative (anti-)self-dual Yang-Mills equation, which implies the noncommutative version of Richard Ward conjecture. The integrability and the relation to string theories are also discussed.

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