Kouichi TODA
Department of Mathematical Physics,
Toyama Prefectural University,
Kurokawa 5180, Kosugi, Imizu,
939-0398, JAPAN
E-mail: toda@pu-toyama.ac.jp

Institute of Physics, University of Tokyo, Komaba,
Meguro-ku, Tokyo 153-8902, JAPAN
E-mail: hamanaka@hep1.c.u-tokyo.ac.jp

Towards noncommutative integrable equations

We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (2+1)-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 equations, which implies the noncommutative version of Ward's conjecture.