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 ${\mathcal {E}}$, 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 ${\mathcal {E}}$ whose flow could be used to embed $\alpha$ into a nontrivial 1-parameter family $\alpha _{\lambda }$ of zero-curvature representations of ${\mathcal {E}}$. 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