On the bi-Hamiltonian Geometry of WDVV Equations
Mathematical Physics
2015-07-14 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove that these systems possess a compatible pair of local homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and third order, respectively).
Keywords
Cite
@article{arxiv.1409.7647,
title = {On the bi-Hamiltonian Geometry of WDVV Equations},
author = {M. V. Pavlov and R. F. Vitolo},
journal= {arXiv preprint arXiv:1409.7647},
year = {2015}
}
Comments
21 pages, revised published version; exposition substantially improved