We discuss, in the framework of the Dubrovin–Zhang 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.
Falqui, G., Lorenzoni, P. (2012). Exact Poisson pencils, $\tau$-structures and topological hierarchies. PHYSICA D-NONLINEAR PHENOMENA, 241, 2178-2187 [10.1016/j.physd.2011.11.009].
Exact Poisson pencils, $\tau$-structures and topological hierarchies
FALQUI, GREGORIO;LORENZONI, PAOLO
2012
Abstract
We discuss, in the framework of the Dubrovin–Zhang 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.
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