The Darboux transformation is used to obtain multisoliton solutions of the chiral model in two dimensions. The matrix solutions of the principal chiral model and its Lax pair are expressed in terms of quasideterminants. The iteration of Darboux transformation gives the quasideterminant multisoliton solutions of the model. It has been shown that the quasideterminant multisoliton solution of the chiral model is the same as obtained by Zakharov and Mikhailov using the dressing method based on matrix Riemann-Hilbert problem.

We use binary Darboux transformation to obtain exact multi-soliton solutions of principal chiral model and its noncommutative generalization. We also show that the exact multi-solitons of 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.

The Darboux transformation of a supersymmetric principal chiral field model in two dimensions is studied. We obtain exact superfield multisoliton solutions of the model by means of iterated Darboux transformation and express them in terms of quasideterminants.

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Abstract. The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.