Exact Poisson pencils, $\tau$-structures and topological hierarchies
  We discuss, in the framework of Dubrovin-Zhang's perturbative approach to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of Poisson pencils, called exact Poisson pencils. In particular we show that, in the semisimple case, exactness of the pencil is equivalent to the constancy of the so-called "central invariants" of the theory that were introduced by Dubrovin, Liu and Zhang. 
Gregorio Falqui, Paolo Lorenzoni
nlin.SI math-ph math.MP