We discuss the extension of soliton theory and integrable systems to non-commutative spaces, focusing on integrable aspects of non-commutative anti-self-dual Yang-Mills equations. We present B?cklund transformations for the G = U(2) non-commutative anti-self-dual Yang-Mills equations and give a wide class of exact solutions of them (not only instanton-type solutions with finite action). We find that one kind of non-commutative determinants, quasi-determinants, play a crucial role in the construction of noncommutative solutions. Finally we briefly present some examples of reduction of non-commutative anti-self-dual Yang-Mills equations to non-commutative KdV, NLS and Liouville equations. This is partially based on collaboration with C. Gilson and J. Nimmo (Glasgow).
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