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

In this paper we consider the problem of constructing a 1-parameter family alpha(lambda) of zero-curvature representations of an equation epsilon, by means of classical symmetry actions on a given zero-curvature representation alpha. By using the cohomology defined by the horizontal gauge differential of alpha, we provide an infinitesimal criterion which permits to identify all infinitesimal classical symmetries of epsilon whose flow could be used to embed alpha into a nontrivial 1-parameter family alpha(lambda) of zero-curvature representations of epsilon. The results of the paper are illustrated with some examples. (C) 2015 Elsevier B.V. All rights reserved.