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 ${\alpha }_{\lambda }$ of zero-curvature representations of an equation Failed to parse (unknown function "\protect"): {\displaystyle \protect\mathcal E} , 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 Failed to parse (unknown function "\protect"): {\displaystyle \protect\mathcal E} whose flow could be used to embed $\alpha$ into a nontrivial $1$-parameter family ${\alpha }_{\lambda }$ of zero-curvature representations of Failed to parse (unknown function "\protect"): {\displaystyle \protect\mathcal E} . The results are illustrated with some examples.