Noncommutative Solitons and Integrable Systems

Abstract

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

References in corpus (2)

• Energy Crisis or a New Soliton in the Noncommutative CP(1) Model?
• Gauge theories on noncommutative spaces

Cited by in corpus (6)

• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Time-Space Noncommutative Abelian Solitons
• A new approach to deformation equations of noncommutative KP hierarchies
• Noncommutative Integrable Systems and Quasideterminants
• Noncommutative Vortices and Instantons from Generalized Bose Operators
• Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories