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arXiv · hep-th/0211148

Towards Noncommutative Integrable Systems

Masashi Hamanaka·Kouichi Toda
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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.

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Masashi Hamanaka, Kouichi Toda. 2003-07-18. Towards Noncommutative Integrable Systems. https://doi.org/10.1016/s0375-9601(03)01138-1

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