We will consider systems of PDEs endowed with a pair of compatible Hamiltonian operators of differential-geometric (Dubrovin-Novikov) type of first and third order respectively. We will describe the structure of the third order operator in flat coordinates of the first order operator. We use this description on a simple example, the WDVV equation in three components (Ferapontov et al.), where we are able to find a Lagrangian representation according with Nutku and Pavlov (arxiv:0108214). With the same description we tackle a 6-component system recently introduced by Sergyeyev and Pavlov (arXiv:1204.2514, oriented WDVV associativity equation) which has only one known first-order Hamiltonian structure and find evidences of a second third order Hamiltonian structure of the above type.
On the bi-Hamiltonian structure of WDVV equations
Research Group:
Speaker:
Raffaele Vitolo
Institution:
University of Salento
Schedule:
Wednesday, March 13, 2013 - 14:15 to 15:00
Location:
A-136
Abstract: