Dubrovin-Novikov Hamiltonian operators and Hamiltonian systems of PDEs
Raffaele Vitolo (University of Salento)
Thursday 23rd November, 2017 15:30-16:30 Maths 311B
The aim of this seminar is to give a systematic way to find determining equations for the compatibility conditions between Dubrovin-Novikov Hamiltonian operators and Hamiltonian systems of PDEs.
Dubrovin-Novikov Hamiltonian operators are a class of Hamiltonian (pseudo)-differential operators. Such operators have differential-geometric and projective-geometric interpretations. Systems of PDEs that are Hamiltonian with respect to a Dubrovin-Novikov Hamiltonian operator are quite common in Mathematical Physics; however, the determining equations for the compatibility conditions between the operators and the systems are known only for first-order operators and for hydrodynamic-type systems. In this lecture we will describe a technique for the systematic derivation of the compatibility conditions. As an example, we will show a new interesting class of hydrodynamic-type systems of PDEs which admit a projective-geometric interpretation.