Towards Noncommutative Integrable Systems
Abstract
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.
Cite
@article{arxiv.hep-th/0211148,
title = {Towards Noncommutative Integrable Systems},
author = {Masashi Hamanaka and Kouichi Toda},
journal= {arXiv preprint arXiv:hep-th/0211148},
year = {2010}
}
Comments
13 pages, 1 figure, LaTeX; v2: typos corrected, comments and references added; v3: comments and references added, version to appear in Phys. lett. A