Noncommutative Solitons and Integrable Systems
Abstract
Description
We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter part is a report on recent results of existence of infinite conserved quantities and exact multi-soliton solutions for noncommutative Gelfand-Dickey hierarchies. Some examples of noncommutative Ward's conjecture are also presented. Finally, we discuss future directions on noncommutative Sato's theories, twistor theories and so on.
27 pages, LaTeX, 3 figures, v3: references added, to appear in proceedings of the COE workshop on Noncommutative Geometry and Physics, Keio, February 26 - March 3, 2004
27 pages, LaTeX, 3 figures, v3: references added, to appear in proceedings of the COE workshop on Noncommutative Geometry and Physics, Keio, February 26 - March 3, 2004