and
Masashi
HAMANAKA
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
Abstract:
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.