Noncommutative Integrable Systems and Quasideterminants
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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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Cited by 1 Pith paper
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Symmetries and reductions on the noncommutative Kadomtsev-Petviashvili and Gelfand-Dickey hierarchies
Constructs additional flows forming W_{1+∞} for noncommutative KP, builds source hierarchies and constrained versions, generalizes to Gelfand-Dickey with new odd/even C-type systems, and derives string equations.
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