Bäcklund Maps in View of the Theory of Connections

Study of Bäcklund transformations is one of the most interesting topics in the theory of partial differential equations. These transformations are used for searching of solutions (in particular, soliton solutions) of nonlinear equations. At the same time Bäklund transformation is the instance of differential-geometric structure generated by a differential equation.
The notion of Bäcklund transformation is a particular case of more general notion of Bäcklund map. In the present work the theory of Bäcklund maps is treated as a special chapter of the theory of connections.