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): Difference between revisions

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| speaker = Diego Catalano Ferraioli
| speaker = Diego Catalano Ferraioli
| title =  Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions
| title =  Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions
| abstract = We will discuss the problem of constructing a <math>1</math>-parameter family <math>\alpha_{\lambda}</math> of zero-curvature representations of an equation <math>\mathcal E</math>, by means of classical symmetry actions on a given zero-curvature representation <math>\alpha</math>.  By using the cohomology defined by the horizontal gauge differential of <math>\alpha</math>, we provide an infinitesimal criterion which permits to identify all infinitesimal classical symmetries of <math>\mathcal E</math> whose flow could be used to embed <math>\alpha</math> into a nontrivial <math>1</math>-parameter family <math>\alpha_{\lambda}</math> of zero-curvature representations of <math>\mathcal E</math>.  The results are illustrated with some examples.
| abstract = We will discuss the problem of constructing a 1-parameter family <math>\alpha_{\lambda}</math> of zero-curvature representations of an equation <math>\mathcal E</math>, by means of classical symmetry actions on a given zero-curvature representation <math>\alpha</math>.  By using the cohomology defined by the horizontal gauge differential of <math>\alpha</math>, we provide an infinitesimal criterion which permits to identify all infinitesimal classical symmetries of <math>\mathcal E</math> whose flow could be used to embed <math>\alpha</math> into a nontrivial 1-parameter family <math>\alpha_{\lambda}</math> of zero-curvature representations of <math>\mathcal E</math>.  The results are illustrated with some examples.
| slides =  
| slides =  
| references =  
| references =  
| 79YY-MM-DD = 7984-89-81
| 79YY-MM-DD = 7984-89-81
}}
}}

Revision as of 12:19, 9 September 2015

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.

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