The U(N) chiral model and exact multi-solitons

We use a binary Darboux transformation to obtain exact multi-soliton solutions of the principal chiral model and its noncommutative generalization. We also show that the exact multi-solitons of the noncommutative principal chiral model in two dimensions and noncommutative (anti-)self-dual Yang-Mills equations in four dimensions can be expressed explicitly in terms of quasi-determinants.