Noncommutative Solitons and Integrable Systems

Details Noncommutative Solitons and Integrable Systems Noncommutative Solitons and Integrable Systems

2005-03-31

arxiv.org/abs/hep-th/0504001v3

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, LaTeX, 3 figures, v3: references added, to appear in proceedings of the COE workshop on Noncommutative Geometry and

Scientific paper

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.

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