# Catalano Ferraioli D. Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

We will discuss the problem of constructing a 1-parameter family ${\displaystyle \alpha _{\lambda }}$ of zero-curvature representations of an equation ${\displaystyle {\mathcal {E}}}$, by means of classical symmetry actions on a given zero-curvature representation ${\displaystyle \alpha }$. By using the cohomology defined by the horizontal gauge differential of ${\displaystyle \alpha }$, we provide an infinitesimal criterion which permits to identify all infinitesimal classical symmetries of ${\displaystyle {\mathcal {E}}}$ whose flow could be used to embed ${\displaystyle \alpha }$ into a nontrivial 1-parameter family ${\displaystyle \alpha _{\lambda }}$ of zero-curvature representations of ${\displaystyle {\mathcal {E}}}$. The results are illustrated with some examples.