Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries, talk at WASCOM 2011 (Brindisi, Italy), 13-16 June 2011 (abstract)

Speaker: Raffaele Vitolo

Title: On the relationship between integrability structures and higher symmetries

Abstract:
It is generally agreed that a system of (non-linear) differential equations is said to be integrable if there exists an infinite sequence of commuting generalized symmetries. Such a sequence can be generated through differential operators like recursion operators, (commuting pairs of) Hamiltonian operators or symplectic operators. In this talk a new method for finding such operators will be presented. It amounts at computing the operators as generalized symmetries of a system of (nonlinear) DEs which is obtained from the initial system of PDEs $F=0$ by adding the equations $\ell _{F}(q)=0$ or $\ell _{F}^{*}(p)=0$, where $\ell$ stands for the linearization and $\ell ^{*}$ stands for its adjoint. Many examples of computations for evolutionary and non-evolutionary equations will be provided.

Slides: Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries (presentation at WASCOM 2011, Brindisi, Italy, 12-18 June 2011).pdf