Applications of Darboux transformations to the self-dual Yang-Mills equations

The linear problem associated with the self-dual Yang-Mills equations is covariant with respect to Darboux and binary Darboux transformations of almost classical hype. This technique is used to construct solutions of the problem in the form of Wronskian-like and Gramm-like determinants. The self-dual conditions can be properly realized for only the latter type of solutions.