Noncommutative integrable systems and quasideterminants

摘要

We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quan-tities and exact soliton solutions for many noncommutative integrable equations, which are rep-resented 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.