Noncommutative Integrable Systems and Quasideterminants

Details Noncommutative Integrable Systems and Quasideterminants Noncommutative Integrable Systems and Quasideterminants

2010-12-29

arxiv.org/abs/1012.6043v1

Physics

Mathematical Physics

16 pages. Based on invited talks at the World Conference on Nonlinear Analysts (WCNA), Orlando, 2-9 July 2008 and the Internat

Scientific paper

We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative integrable equations, which are represented in terms of Strachan's products and quasi-determinants, respectively. We also present a relation to an noncommutative anti-self-dual Yang-Mills equation, and make comments on how "integrability" should be considered in noncommutative spaces.

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