Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions

In this paper we consider the problem of constructing a 11-parameter family αλαλ of zero-curvature representations of an equation EE, by means of classical symmetry actions on a given zero-curvature representation αα. By using the cohomology defined by the horizontal gauge differential of αα, we provide an infinitesimal criterion which permits to identify all infinitesimal classical symmetries of EE whose flow could be used to embed αα into a nontrivial 11-parameter family αλαλ of zero-curvature representations of EE. The results of the paper are illustrated with some examples.