# 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)

**Speaker**: Diego Catalano Ferraioli

**Title**: Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions
**Abstract**:

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

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