Speaker
Dr
Vitolo Raffaele
(Universita' del Salento)
Description
The well-established method of tangent and cotangent covering for
searching integrability operators, like Hamiltonian, symplectic and recursion
operators, was introduced by Kersten, Krasil'shchik and Verbovetsky in
2003. The method consists in describing integrability operators of a given PDE
as linear functions of some odd variables which are in the kernel of
linearization or adjoint linearization of the PDE. We apply the method to the
search of Dubrovin-Novikov integrability operators for hydrodynamic-type PDEs.
We recover known results, like: Tsarev's compatibility conditions between a
hydrodynamic-type system and a first-order local Dubrovin-Novikov Hamiltonian
operator; a geometric interpretation of nonlocalities in Ferapontov's nonlocal
homogeneous operators. We obtain new results, like a new system of PDEs that
expresses the compatibility of third-order Dubrovin-Novikov and a
hydrodynamic-type system, as well as new (integrable?) systems of that type. We
will discuss several interesting problems and conjectures that are emerging
from the interaction between the two theories.
Primary author
Dr
Vitolo Raffaele
(Universita' del Salento)
